Deirdredolores

Hope its not too late to add my two cents! We did a similar trip not long ago and my suggestions are as follows:
Stay at Old Sydney Holiday Inn, George Street in "the Rocks" in Sydney. Very near Circular Quay, Opera Hse, old pubs + lots of history. Short walking tours very informative.
Visit Alice and Uluru. We took Emu Run tours: full of info + fun. Wonderful champagne/dinner watching sunset.
We skipped Cairns instead stayed in Airlie Beach, 2 hrs north. Overnight in Sunlit Waters studio apt. great. Boarded Whitsunday Magic (fantastic food and service) for 3 days aboard sailing and non-touristy reef. Really was magic snorkeling (we've done lots). Different fish + giant clams in outer reef from inner reef, check it out. Enjoy.
PS We took The Ghan train to Alice + visited Kangaroo Island both fabulous but don't think you have time.

howland

Another suggestion - we are spending 3 days at Heron Island which is on the Great Barrier Reef and not as far to get to as Cairns and from there going to Kangaroo Island.

ivenotbeeneverywhere

Howland - Heron island is more expensive getting to than going to Cairns, it has less flights and because they are via one of Australia's most forgettable towns the costs are higher. The Whitsundays are far, far better, more diverse, are closer than Cairns but Cairns has a lot of other things in the surrounding areas that the Whitsunday's and of course Heron Island. I note that you are going to Kangaroo Island ( what is it with that place? Does it get priority advertising or something or is it just because of its name people think it has more wildlife?). The Atherton Tablelands in the hills above Cairns has far more wildlife than Kangaroo Island will ever have in a millenium. Also getting to Kangaroo Island is expensive when you are already on the eastern seaboard.

peterSale

ivenotbeeneverywhere - Good point on Kangaroo Island. It IS a fantastic place, but there seems to be many people willing to travel out of their way to get there. I think it is a great place but in reality many of the things it offers can be seen elsewhere, with the exception of walking amongst the seals. But still a long and expensive side trip for an hour's tour. The KI tourism board is obviously doing a good job.