You can pitch a tent on a few very out of the way beaches, but Bondi and most other places definitely don't qualify as out of the way.
Tents are OK on the northern part of Fraser Island but it's virtually impossible to get there going via 4WD. The southern part of Fraser isn't very nice at all and it's a long and difficult hike to get to the northern part and you'd be dodging heavy traffic on the beach the whole way. The beach running from just above Noosa Heads to Double Island Point (just south of Fraser Island) is beautiful and tents are OK there, but getting there is a problem though it is possible. Make sure you enquire about camping permits etc or the rangers will get you.
The EPA website has info about National Park and State Forest camp grounds in Queensland:
http://www.epa.qld.gov.au/parks_and_forests/find_a_park_or_forest/
Other states will have similar sites.
You'll find cheap camping grounds all along the coast both privately run and in National Parks and which range from about $10 per night for 2 people with a tent and no vehicle.