Thanks for the comments. I'm glad to hear Oz has taxis, I was thinking we would have to hire a horse and buggy!
In all seriousness, Taxi or shuttle will probably work best for us. We may rent a car eventually, but we will be flying in and staying only two nights before a 3 day liveaboard on the GBR. We are considering a day trip to Kuranda on the day between our arrival in Cairns and our liveaboard, but it doesn't seem like we will need a car for it (I have seen packages with Train, Skyway Tram, Tjapukai Aboriginal Park, and hotel transfers all included).
On return from the boat, we will stay one additional night in Cairns and then move to environs north (Port D., Mossman, Daintree, etc.) We will probably rent a car for this part.
Sorry for hijacking your thread elbidercni, but thanks everyone for the info.