First, you should let us know exactly what you mean by "backpacking." If you are just talking about traveling on the cheap with a pack, there are other travel sites such as Lonely Planet, the book publisher, with better info than you will likely get here.
This site is a hiking site, not a general travel site. Doesn't mean some of us haven't done it, just not what this site is all about.
The last time I was down in Oz was years ago. I was up and down the East Coast-Sydney, Brisbane, the Gold Coast, Melbourne, Cairns, Canberra. I took the train, bus, got rides from people I met and hired a car for a few days.
It is easy to get around, but flying is expensive. I didn't really do any camping, but there are plenty of places to camp.
Get a good guidebook, like the Lonely Planet or Insight book and start planning with them. Don't forget the seasons are opposite ours.
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Don't get me started, you know how I get.