Whilst Virgin is setting up in Australia, they are setting up a discount carrier like their Brussels based subsidiary Virgin Express. They are not setting up a full service carrier like Virgin Atlantic. For example the 733s will all be configured in a charter layout (ie no legroom), some of their terminals will be in demountables, they will have no business lounges and they are only operating between 3 or 4 Australian ports.
It is unlikely that SQ will want to transfer their high paying premium customers onto a service like this and will probably prefer to keep the current arrangement they have with Ansett. All SQ flights between SIN and Australia are already AN codeshares.