I was in OZ in May for two weeks (then in NZ for another week). Wish that I'd been certified then, but did Discover while we were there, came home to get my certification (checkout dive is in two weeks!). My husband and I drove from Airlie Beach to Port Douglas. It wasn't too bad, but as others have said - do not underestimate the craptacular road conditions and construction. The first day that we had our rental car (spent a week in Gold Coast with my aunt, then flew to Airlie) we drove from Airlie Beach to Townsville. Google maps claims it takes 3 hours 16 minutes. It took us EIGHT HOURS. I was shocked that a major highway was tar and chip for most of it. The major highway looks like the little country road that I live on.
My advice would be to fly into Brisbane, get acclimated there and do some diving (others mentioned Moreton and Pembroke Island). Then fly to Airlie Beach, do a liveaboard and some partying... rent your campervan and go north from there. Maybe a liveaboard from Townsville and/or Cairns/Port Douglas.
That's how I'll do it next time!
---------- Post added September 12th, 2013 at 11:35 AM ----------
I plan to have A/C in the vehicle.
When is NOT cyclone season?
I'm pretty sure that cyclone season and the wet season coincide, November-March/April.
I found it quite comfortable in May. We were in 3mm wetsuits in Coolangatta and 5mm shorties in Port Douglas.
The other thing to consider are the stingers. Stinger season also coincides with the wet season, although you should wear a wetsuit at all times anyway. Stingers don't care what season it is and would love to screw up your trip.