There are a number of reasons behind this. Constitutionally, politically, historically, geographically, socially, and pragmatically, there is little reason to believe that Canada will follow in the footsteps of Australia. Indeed, Canada will never abandon the Monarchy- at least Canada in its current form.
First, constitutionally, it would open way too many cans of worms. Quebeckers (The French as you have put it, QFA380), have a strong case for not only eliminating the Monarchy, but many also feel that they ought to be independent of Canada. If the ROC
(Rest of Canada) were to start tinkering with the Monarchy, Quebec separatism would complicate the issue immensely. The complications would be greater still, once you factor in the desires for self-government of the First Nations peoples (Canada's Aboriginals) in the face of their long-standing grievances and claims against the Crown. The upheaval for those who benefit from the status quo would be just too great.
As a generality, I agree with the above post that explains that we accept as a good thing the fact that the Head of State and the Head of government are two different people occupying two different offices. It's good to know that while the government is, for all intents and purposes, responsible to us citizens, there is a single individual that is responsible for ensuring that fact where that person can, although Constitutionally dangerous as it ought to be, intervene in the case of an emergency or in the face of perceived abuse of power- just as the Governor General did in 1926 in the King-Byng Affair in Canada, or in 1975 in Australia between Kerr and Whitlam.
Second, politically, Canada has gone through a couple of gut-wrenching, angst-ridden attempts at Constitutional change since the 1980s and both times the economy went to Hell in a hand-basket while the government's eye was on the constitutional ball. The bickering between the provinces and the federal government dominated the newspapers not just for days and weeks, but for months and years. The last attempt- the Charlottetown Accord was soundly defeated in a referendum by Canadians despite being supported by all corners of the political establishment- again after months of wrangling and horse-trading. Constitutional change in Canada is messy and unpleasant. And every dirty dark Canadian secret gets drawn into the debate- and our secrets are as shameful as South Africa's under Apartheid.
Guaranteed, even the thought of more constitutional talk will send the most reserved, quiet and happiest of Canadians into fits of under-breath explicatives and cursing that would make the most seasoned sailors blush. Because of this, even the most outspoken politicians, the fools that they are who rush in where angels fear to tread, give this one a wide berth. So far, the most we've seen at re-inventing our institutions in latter years has been a recent proposal to reform the Senate (our version of the House of Lords) where members might only sit for seven years, instead of a life-time until they're 75. But even that's not radical change. Senators will still be appointed by the prime minister from a 'suggested' list of nominees.
Thirdly, historically Canada's creation was a reaction to the expansionist aspirations of the revolutionary republic to the South, namely the USA. Those loyal to the King in the revolution headed North and as such there is still a very strong undercurrent of loyalty to the crown in certain pockets of the population. Given the vast distances in Canada, we tend to be somewhat parochial in our thinking and these loyalists hold a lot of sway in their respective spheres of influence. Additionally, the presence of the Monarchy underlies the differences (few but significant) that exist between Canadians and Americans. We as Canadians often define ourselves by what we are not; how we differ from Americans (this is often seen in the non-av forums).
Another historic fact, as discussed by others in this thread, concerns the fact that Canada has evolved with the Monarchy front and centre. We have the Hudson's Bay Company. The Royal Canadian Mounted Police. When Britain declared war on Germany in the First World War, Canada, like Australia, was automatically at war too, Canada earned its foreign policy independence on the battlefields of France, fighting for the British Empire.
Fourthly, with this historic background, the geography and demography that Canada finds itself is very different from that of Australia. First, it shares the longest supposedly undefended border with the strongest, most boisterous, internationally activist yet isolationist republic in the world. As a collective, we are somewhere between tacitly complacent to jubilantly 'North Americans' and as such, independently-minded and isolated from the rest of the world. Because of that proximity- something no other country gets to have except Mexico and there's hardly a parallel there, we get special consideration in Washington D.C. as continental brothers so we get to play at being "American" without being Americans- a status Canadians cherish whether they'll admit it or not. Whether there's real benefit for either side in that relationship is perhaps for another thread at another time.
But we also have our roots to the Commonwealth and the historic stability that comes with the Monarchy. While very insecure about ourselves about a lot of things, Canadians are quite comfortable with it all. We see ourselves as having an egalitarian society so Class is not so much an issue- all the Class baggage that exists under 'She who Reigns Over Us' simply doesn't make it across the Atlantic. At least in the initial stages, Canada was not a penal colony (sorry but that is the truth)... it was always a promised land for those who wanted a fresh start but who still wanted to stay within the British sphere of influence in the Americas.
Fifth, social references have been made in this thread and often elsewhere that the Queen is a lovely old lady who drops in for a visit every so often to cut ribbons and has her portrait on our coins. She represents a concept in Canada rather than a Dynasty as her lineage hasn't been present in Canada since the 1950s when Vincent Massey was made Canada's first Canadian Governor General.
Unlike in Australia (or so I believe), there is no schizophrenic relationship with Britain here in Canada. We drive on the right like the contientals and Americans. We have our own flag. There are no pilgrimages to the Old Country any more. Importantly, Royal titles cannot be held by Canadians. Most recently, Conrad Black, Lord Black of Crossharbour, had to renounce his Canadian birthright and citizenship to sit as a member of the House of Lords. We don't represent 'civilization' in a distant part of the world nor clamour to do so. We don't see ourselves as breaking away from the stodgy old family as we are quite comfortably a part of that family. We are still close enough to Britain physically to actually share in its own growth and evolution.
Finally, as a pragmatic people, simply the cost is too prohibitive. Until something else comes along that will provide the same benefits at less cost (which is impossible since there are only 11 offices to support- one Governor General and 10 Lieutenant Governors, one for each province). Check this page out for a break-down.
Given that the British public pays the entire bill to maintain the Royal Family in the style to which It has become accustomed, we actually get all the pomp and circumstance, as well as the hidden benefit of 'Peace, Order and Good Government' without the cost. Unlike Canadians, Australians apparently don't see that as a saving grace.
So to conclude, it will many years before Canadians drop the Monarchy- if ever. Constitutionally it would be too difficult in the face of widespread opposition to any constitutional tinkering. Historically, Canada's institutions and polity are borne of the Monarchy in reaction to the republic to the south and as such it is very deeply engrained in our society. The Monarchy, as a concept, has served us well. Geographically, we are at once equally North American and global thanks to our close relationship to the United States and historic ties (without the apron strings) to Britain. And finally, we're cheap and for a Canadian, if it affects the pocketbook negatively, you can work on the assumption that it won't happen.
As a footnote, that day might come should we have a reformed Senate. Given that in Australia your Senate is also elected (something that ours never shall be as its just too plummy a patronage appointment for any current government to abandon), there is no institutional inertia or reason to keep on with the tried-and-true. You have cast off that brake in Canberra (heck- you even invented a post-British Empire capital city!- something unthinkable in Canada) and now unfettered you are looking about for a stronger sign of independence and severing ties with the Monarchy is a logical step.
Possibly, with a reformed senate there will come a day in Canada when there is a parliamentary move to abolish the Crown but that day, I'd say QFA380, won't happen even in your lifetime.
Just my $2.50 worth.