Air North did in fact use to operate the Goonie Bird until a few years ago on scenic flights. But no more unfortunately. I am not even sure who operates the DC-3s that they use to have, as we now have quite a few DC-3 scenic operators here in Australia now.
Airnorth Regional (as the company is now known) has a website www.airnorth.com.au but they now only operate scheduled commuter operations.
VH-MMA is owned by the Vintage Aircraft Company. I do not have a phone number for them and a call to directory assistance came up blank, but I do have an address for them (I think it may be a personal address) of:
10 Giles Street
Fannie Bay is a suburb of Darwin. It may be worth your while contacting them when you go to Darwin.
I took the Goonie Bird tour back in 1991 and it was a great flight. I have some of the memorabilia they hand out on board, postcards, certificates, etc.
If you are interested in other scenic flights in Darwin, I heard that there are some Grumman G-73 Mallards (seaplanes) operating flight seeing tours in Darwin. From what I can remember they are now operated by Pearl Aviation. This is unconfirmed of course, but you might want to email Pearl Aviation's head office in Perth at email@example.com to get some firm information from them.
If you are travelling elsewhere in the Northern Territory I can recommend Kakadu Air for flightseeing tours. firstname.lastname@example.org They only operate Cessna 207 Stationair's, but there flights are great, taking in Kakadu National Park out of Jabiru.
Sorry I couldn't be of more help, but I hope this helps you some what. You may also want to check out the Northern Territory Tourist Commission www.nttc.com.au and see if they can't give you more information. They are very quick in responding to emails so give them a go too.