Might be a tad difficult to find somwhere secluded at that time of year with all the ammenities you have mentioned. I would hazard a guess and say the beaches would be fairly busy so maybe somewhere in Nth NSW may fit the bill. A friend mentioned a place called http://www.wavehillfarmstay.com.au
that may fit the bill but it would appear that a $wd is necesary to access the camping grounds and it maybe a three hour drive from Brissy. Good luck with your search.
Please sir, Can I have some more? Time off that is.
"Hard at it"
Fruit Bat Falls, Cape York