A little further north are Caboolture, Caloundra & Maroochydore. West of Brissy at the top of the escarpment is Toowoomba. All bit further to drive but just in case you wish to expand your options.
Redcliffe Aero Club has a good reputation. Been 20 years since I worked there but from what I've read of other's more recent experience that doesn't seem to have changed.