Hi Charmaine -
Sounds like you had a great time! I'm not familiar with Hamilton Island but sounds like it'll be good for all of you - you get some time by your self and with hubby and Rory will get some playtime activities. Evven getting an hour to yourself on holiday is always a GREAT thing!
Being in Alice is pretty good. I've not been to Uluru but know people who've been with little ones and it's good if you have a baby backpack to carry them in. You do the walk around and they eventually fall asleep in the back pack. Kings Canyon is supposed to be better for the walking treks and prettier than Uluru.
As far as things to do in Alice, I could be busy with something every day with the boys if I never wanted a day at home...
The Desert Park is great for kids to walk around, see the animals...you get the picture. The Reptile center is interesting but that might be a bit old for Rory but you might like it. There is a indoor play gym sort of thing called Squiggles. And there is some sort of play group or kid thing going on almost everyday but those would probably be hard to find out about for a visitor. Also the telegraph station is nice to visit. Lots of room to run around, some good walking tracks and hike up a little mountain (more of a rock pile but mountain sounds much cooler to a 2 yr old
) Also, drives out to Simpson's gap, Standley Chasm and Glen Helen are nice too. Kids get a work out walking around, spotting lizards and such.
There are non kids things like the Royal flying doctor service tour, the School of the air, and general souvenir shopping (although normal everyday shopping is not the towns strong point!)
I don't know of any places that have drop in child care services but if you break the day up, it wouldn't be too bad.
It's getting cold here now but I definitely don't recommend coming here in the summer! The heat is too crazy for little guys as they get pretty cranky. And the flies are HORRIBLE! Something to consider...
Hope you have a good time at Hamilton Island.
Cheers,
Kristin