I don't backpack, but wotif.com shows backpack hostels starting at $21 a night, but the "nicer" ones are $40/night -- for a 6-bed dorm room. Meals are $10-15 in pubs or fish and chips food for filling and decent food, so I'd say $60/day is a more realistic bare minimum. But you need bus/train/ferry tickets unless you plan to walk everywhere, which would take it up to $100/day quickly. I'd say you'd need to stay with friends to spend less than $2000 for a 3 week trip anywhere in Oz. Most backpackers come for a few months and work, also buy a car (for as little as $500); it certainly is an organized activity in Australia, so a good place for backpacking but it isn't cheap like Asia.