Whitsundays means Hamilton Island which is perfect if you've got children and is family friendly. You can go to Whitehaven Beach, although I'm not sure how the baby will cope with the boat rides so you'd better check with Hamilton Island first. It's all owned by the one entity so has a combined website.

Cairns is just a stopping off point to get to other places. It's pretty blah in of itself unless you're a backpacker and want to get hammered 24/7

I doubt you'll be allowed to take a baby out to the reef as they are very safety conscious but check with the operators - there are several, just google.

All of Queensland will be hot but more importantly, steamy as it's the rainy season.

I'd head to Tasmania if you like quaint. It's very easy to drive around. Go to Freycinet - spectacular but you won't be able to go to Wineglass Bay unless you carry your baby, so bring a carry pack. It's quite a walk.

Sydney is a fun, big city and is stunning. It can be hot and steamy at that time of year but it's still beautiful. Melbourne is very European and the capital of cool, lots of cafes and restaurants- the top level ones won't let you bring a baby and you won't want to. Melbourne will be hot but dry. You could actually drive from one to the other via the coastal roads and stay along there. Merimbula, Batemans Bay, Jerivs Bay, Ulladulla and Kiama and everything in between is really quite stunning and at that time of the year will be the best places to be weather wise. It'll still be hot.

Enjoy your time downunder.