There's a lot of things to do in Australia that doesn't require you going as far out as New Zealand! Just check out this
list.
Just make sure you have enough time to see/do all that you plan! You can fly into Sydney, being that it one of the bigger cities, then fly off into Cairns like fmica said but that just all depends on what you plan to do. Beaches, Surfing, Hiking, it's all up to you!
I do recommend, though, that you at least visit the Sydney Opera House seeing as how that is iconic to Australia.