I'm gonna say that the outback would be great, central western NSW would be good, and as said above the High Country is absolutely stunning at that time of year albeit bloody cold.
As for my beloved Tasmania, naturally there is no bad time to visit, but I would say the best time is March to May with April probably the peak. The large number of deciduous trees in autumn foliage combined with eucalypt forests combine to make great photography, and the light at that time of year is stunning.
It's also the time of best weather, before the cold sets in but after the hot dry summer.
Winter is all about bare branch trees and snow capped mountains, black and white heaven.
Everything browns off in summer.
Spring is often windy with lots of frost and fog and still snow on the mountains, but new growth everywhere looks great too.
In all likelihood I would be travelling by plane or train, but I like the idea of having my own transport in the Uluru area, specifically to get great light. I did use a tour there many years before, but of course was limited to where they drove us, at what time of day, and the fact that it rained every day in the Simpson Desert while I was there.
Although I'm not adverse to driving long distances through the middle of nowhere (done it many times in Canada after all), I'd probably stick to smaller, more focused areas due to unfamiliarity with the terrain/climate, time, and cost.
In any event, this is still just in the preliminary stages as it all depends if I'm still in Japan next year (!) and, if I am, if I get accepted to the conference I want to present at in Wellington.
Edit: Derwent, just saw your post. I'd love to go to Tasmania -- it's been a dream of mine for many years. I do love the raw, bare nature of winter (my favorite season to photograph), but the weather might be an issue (not as a local, but as a tourist). It's definitely still on the list, but for now it's a wait and see game for me.
My favorite thing is to go where I've never been. D. Arbus
I'd go visit Tasmania.......It's compact, you can travel between many sights in a few hours, and the scenery can be spectacular.
Maybe spend a week in Melbourne, then go down to Tassie for a couple of weeks?
It depends what you want to see..if you are a landscape person then Tassie, if you like people/cities then I'd come to Melbourne (theres also a photo market in September in Box Hill - about 1/2 hour by train from the city centre. It's the biggest photo market in Australia with around 80 tables held in the old Town Hall building)
As a born and bred Melbournian I love Melbourne, but also love wandering around Sydney, but the pace of life can be hectic compared to Melbourne..however in September Sydney will be a bit warmer, and the harbour and coastline are stunning..plus The Rocks is a great area to wander around...