When are you going? Do you prefer urban areas or beaches?

Sydney has its fair share of good Starwood properties. I'd personally recommend the W, although the Sheraton and Westin both get good reviews around here.

Noosa -- and virtually everywhere along the Sunshine Coast -- is beautiful. Definitely worth a few days.

Port Douglas is a great spot but I think Cape Tribulation is better, but you're not going to find any Starwood properties all the way up there. It's well within driving distance though, so you could always fly into Cairns and rent a car there.

Melbourne is a great city, but depending on the time of year, the weather won't be nearly as nice as what you can find farther north. I've only stayed at the Park Hyatt there so I can't comment on any of the SPG properties.

As far as timing is concerned, you could easily spend two nights each in Sydney/Melbourne/Noosa/Port. Obviously you'll be moving around a lot. You could also cut one or two places out and just focus on a couple of places but it really depends on what kind of trip you're after. Just about all of these properties have been covered rather extensively on this forum, so a search will also yield a great deal of information.