It takes a little bit of effort to get across to Fraser Island - you need a four wheel drive vehicles and to catch a barge across - but it is worth it. If you manage to go during the wheel out of school holidays, you'll find it very quiet.
The campsite at Central Station is a great place to set your base up. It is in the middle of the island, so a good spot to visit all the inland lakes from without having to worry about the tides on the beach. You can also walk to Basin Lake from here, and do some other short walks.
It is fenced from dingoes, has coin-operated hot showers, and most campsites come up their own picnic tables with shared sink facilities, making camping a little bit easier and all the rainforest surrounding the camp site makes it very shaded, so there's no getting woken up with the sun. Campsites can be booked online.