Obtain a visa to visit Australia. This can be a tourist visa or a working holiday visa.
Get a room at a hostel. In Australia, accommodation is easy to find. There are backpacker hostels throughout Brisbane that are relatively inexpensive. You will have to provide your own meals, though.
Work at the hostel where you are staying. This usually entails manning the office or cleaning the rooms and facilities; however, the pay may simply be free accommodations.
Find work at a restaurant. Cafes and diners, usually the ones that stay open late or 24 hours, will usually have positions for waitresses and cooks. Most of these will expect you to work at least 3 months, preferably 6 or more.
Do some seasonal work. Seasonal work on small crop farms can be found about 300 miles north of Brisbane at Childers and Bundaberg and other similar centers on the Bruce Highway (the main road in Eastern Australia). Childers, a small town in the Wide Bay district of Queensland, is especially set up to cater to backpackers and working holiday travelers.
Check out government resources. The hostels often have contacts to available work in the area, but the government employment service (Centrelink) will have work listings as well. Tourist centers all over Eastern Queensland have a similar infrastructure in place, and hostels have lists of employers who are seeking workers.