Well would you have to fly out of the same city? Or can you do an open jaw. If I were you I would probably fly into Cairns, travel down the east coast, Sydney to Melbourne, Tasmania, Great Ocean Road to Adelaide, Adelaide to Darwin (do uluru trip), Darwin to Perth (Kakadu, Kalbarri, Coral Bay...etc)..
From Perth you can go south for a few weeks. the margaret river area. Then you would basically be seeing all or lots of australia.
Perth and the west coast is beautiful!!! It was actually my favourite part of australia. I found it to be so much more real. Wasn't full of 19 year old gappers that were getting wasted every single night. I found it was fun of people who were actually wanting to explore Australia in it's finest! Once you have a route in mind follow it and you can settle a couple of times along the way. My advice to you: Don't get stuck for many months in Sydney!!! Have the backpacker population arrives in Sydney and works there for 6 months. WTF! Go out and explore
I have been to: Myanmar, Laos, Cambodia, Thailand, Vietnam, Singapore, New Zealand , Australia, Fiji, Costa Rica, United States, England, Ireland, Wales, Northern Ireland, Scotland , France, Italy, Switzerland, Germany, Austria, Vatican, Guatemala, Belize, Honduras, Nicaragua, El Salvador, Panama, Colombia, Mexico, India, Nepal.
Where to Next? Iceland!