Can't say I've been to Australia but I was engaged to an aussie. We were planning to go to Australia on a tour just before things started to get a little rocky between us and I decided to kick him out.
Anyways, the MUST SEE places of Australia are CAIRNS, MELBOURNE, SYDNEY, GREAT BARRIER REEF.
Check this out:
http://www.ozexperience.com/oz/timetable_index.htmThis company offers cheap tours for backpackers, they do New Zealand and Feejee too, in case you're planning to go there. It's fun, you get to meet nice ppl and stay at hostels with other young backpackers. How do I know this? I used to work at their branch in South America.
Anyways, hope this helps. As far as travelling to Australia, I won't be there for a while.
Good Luck! Have fun.