You don't say how much space you have in any part of the land.
I have tree-loppers coming next Monday to take out one of those I inherited and one of those I planted.
Not that I ever seem to have taken my own advice, but a tree is a substantial investment. And expensive to remove.
As idyllic as it sounds, anything that grows fast enough for your child to be able to climb, is probably going to lift your house off its foundations.
And having visited a couple of people recently with small yards and small children, having an un-disrupted lawn area is really useful for other skills like ball games.
So, I would suggest you forget the tree idea, and instead go for a well-designed play area to one side, with a climbing pole. Shade sale over, or whatever if needed, and sand-pit below. Do some marginal plantings of grevilleas,and maybe one or more of the grafted, small, flowering gums ("summer red"). These will attract all sorts of birds, butterflies and provide a daily treat for your child in watching their antics. If you are in an area that might attract other wildlife - a possum nesting box or keep eyes open for koalas.
Sorry if that's not the answer you wanted, but things can grow mighty fast in Qld, and not always the way you want.

Hi Alison

Thanks for the pointers. We have a fairly big block (1/4 acre) - I am doing the play area too (I have a shade sail that I will soon put back up), just thought a tree would be quite nice.

Might just put in a smaller tree (not a climber) and get a climbing pole.... good suggestion!
Steve