Arrgh where's my green smiley, Rach! That sounds like a brilliant trip - very jealous.
Fraser Island, I believe Orchid Beach in the NW is the only realistic option, there was a thread here recently with a contact number (Orchard beach I think it was referred to), the other strips are controlled by the rangers and I believe you're likely to exceed MTOW dealing with the relevant paperwork!
In that vicinity consider Teewah, Noosa and Rainbow Bay to the south, beautiful areas to fly over - unfortunately I don't have contact details handy, however there have been threads recently referring to these - I think BecM has some connection with Noosa from memory and Rod? from Rainbow Beach made a generous offer a while back (Tomo you corresponded with him).
On the way up there, consider detouring over Moreton Bay to get around Brisbane airspace, spectacular flight and you could land at Cowan-Cowan (Tangalooma strip definitely PPR, call resort for details). If you get caugth out there is a bunk house at Heck Field, Jacobs Well, also caravans at Dunwich on North Straddie I'm told). I'll think of more and i'm sure others will have lots more ideas.
Cheers Carl
PS I'll try dredge up the contact numbers I have for those posted so far.