Okay, probably better to start in Sydney, as Sydney will get colder as the months go on, and the weather in Cairns will get less sticky but still nice and warm by the time you get up there.
I budgeted for a grand a month in Oz, and that worked out fine, I actually spent a bit less than that and ended up doing everything I wanted to and more. If you go and drinking/eating out all the time then it might cost you a bit more, but I'd say you should be able to get by on three K.
I'd say it'd be good to have some places you definately want to go to, such as Whitsundays and Fraser Island, but I wouldn't think about making any rigid plans, because you'll easily meet people when you're over there and come to like/dislike certain places more than others.
3 months is loads for this East Coast... if you've got the money, I'd get over to Alice Springs and see Uluru, The Olgas and Kings Canyon, but if not then I'd recommend spending time in the Northern Beaches (Manly etc) around Sydney, Byron Bay for a few days, Brisbane, Noosa for a few days (Australia Zoo aswell), and doing a trip to Fraser Island from Rainbow Beach, then the Whitsunday Islands, then Magnetic Island up the coast to Cairns.
For hostels, they're everywhere in places like Cairns - most of the places are quite small so they're not hard to find, but when you get over there you can pick up a magazine called
TNT Down Under which has a list of hostels and all the best places to go etc. I wouldn't stress about anything, everything sorts itself out really easily when you get there.
