Cheap domestic flight would be your best bet, I think. It'll probably run you a couple of hundred bucks per person to get to Sydney (try for the cheaper services like Virgin and Jetstar, if the latter run out of there), but the extra money will save you the agonising time spent in a coach or on a train. If, however, you don't mind the time spent in travel, you could always hire a car in Darwin, and drop it off at Sydney or Cairns, and jump from camping ground to camping ground at night--they're not very expensive and, I believe, there is a map of them around online. A friend of mine did it from Bundaberg and had a great time, though it took him four or five days. Car rental might set you back some, though. The cheapest alternative, I believe, is to take a coach, but really, all that time spent in a bus?
If all that fails, hitchhiking gets the nod. All those murderers of visiting foreigners are long caught, or so the TV tells me.
(This is part of the Ask Me A Question, Get An Answer thing I'm doing on this blog. Anything goes.)
