OK, I recommend Magnetic Island for the coast lands. Great way to see the Barrier reef from there and some lovely beach and tracks, etc.
Then try and get to Longreach for the outback experience. If you really want an outback experience, try and get to the Birdsville races.
Birdsville has a population of less than 100 for about 50 weeks of the year and then 3,000 for the other 2 *lol* It's also in driving distance of the largest sand dune in the world (fondly called "Big Red")
I recommend Brisbane's Lonepine Koala sanctuary for a decent zoo. Australia zoo is great for the kids but I reckon you'll get more of your money's worth at the sanctuary. They have heaps of Aussie animals. If you're after some history and sights, Sydney is the place to be. You get the museums and all sorts of heritage places talking of the first fleet, gold rush, Ned Kelly and many of Australia's most Historic sights. You can also climb the harbour bridge and maybe visit the Opera House for some music (It's MASSIVE). For even more country experience, I'd say get to Alice Springs as they generally have all that stuff there with Uluru and all.
Good Luck