I was also thinking the same (and I don't think it's limited to just the Gold Coast either - I think you'd struggle finding many US-style camps all over Australia). Most camps that I'm aware of, as MacKnee has said, are catered for school/youth groups who might book out an entire place. There are school holiday programs, but these would usually just be day activities held somewhere.
There are other camps that I know of, but these are more for those from socially/economically-disadvantaged backgrounds who might not normally have the opportunity to get out and about elsewhere.
Sorry for repeating a lot of what MacKnee has said, as I didn't see their previous post! As for school holidays, QLD school holidays will generally start from late June to early July, but it's only for about 2 weeks or so.
Good luck with your planning and have a GREAT time on the Gold Coast! :)
Edited: 04 January 2012, 14:40