I just completed a similar trip. Dived the Brisbane, drove and snorkeled in the Whitsundays, drove to Ayre to dive the Yongala, drove to Cairns to get on Mike Ball's Spoilsport for what was a fabulous trip (one of the best and I have been on liveaboards in the PNW of US, Mexico, Cocos, and Galapagos). I was told by locals to be careful after diving the Yongala and driving directly to Cairns as there is a high pass through the hills (watch for altitude decompression they advised). Driving allows you to see the great open that is much of Queensland, but it does take a long time (with all that sugar cane I understand where Bundaberg sugar and rum come from). I was advised by people in Brisbane and Townsville, that if I was only going for one day, Port Douglas as a day trip was better than Cairns, but because there is so little in Port Douglas, and what there is tends to be pricey, that I should go with Poseidon and take advantage of the transfer provided for people from Cairns (about $20 dollars if memory serves). Whatever you do, it should be a great trip. I visited many of the dive shops in the CBD of Cairns and, as one who once worked in a dive shop, was very impressed wih each operation.
I did not end up going to Port Douglas as I had enough diving at that point. I did enjoy exploring the Cairns area and did so by public bus and shuttles. Stayed at a budget hotel in North Cairns, but could walk to everything (wasn't too hot yet). When not diving, exploring, or driving, I did discover the wonderful outdoor swimming pools that the communities have.
I am going back within two years. It took me 25 years to get to Oz, I regret waiting so long. I loved it, the diving is fabulous, the dive operations are professional and well run taking pains to make sure the customer gets a quality trip, and the people are great. Now if you could just do something about that pesky exchange rate ($1.07 USD to $1 AUD) before I get back...