If Australia should be discovered and experienced - and it should, then it should be discovered by car.
The climate and the culture is so great that it is a waste to just visit one or two cities, especially if you are taking a plane between them. Sydney, Perth, Melbourne, Brisbane and Adelaide are all cities that deserve thorough experiencing; at least a week in each. And then you still have the whole country side left, where the sun and the breezes are waiting for you.
The best way to go about this is to find a place with cars for sale, and use whatever money you have saved up with your friends, to buy a safe, decent car that can take you around the enormous country. For example, you can use Simpletrade in order to find whatever suits you the best.
Then you pack it with food, blankets, mattresses, tents, water, cameras, bathing suits, a stereo, speakers, towels, maps, you name it. Anything that will keep you warm, safe, entertained and dry, pretty much. It is not overly important which route you take, as long as you try to see all cardinal points. Each part of the country has its own charms.
When it is time to fly back to whatever country you came from, you just sell the car and hopefully you will get most of your money back!