Sweet..
Me and a dive buddy took 2 weeks to drive up the coast from Sydney to Cairns. Beautiful drive, and you can hike different rain forest National Parks every day of your trip.
The diving out of Cairns is ok, but I'd recommend the extra hour north (like 30 miles) town of Port Douglas. Sweet little town, and the dive boats go to better dive spots. Port Douglas is a kind of "vacation" weekend spot for local Aussies apparently. Lot a fun.
Brisbane, don't forget to look up Australia Zoo (near there) Sweet zoo.. Sydney, aquarium is worth the trip..
Didn't go to the Whitsunday Isles, but heard they are beautiful.