I think that any "general" tutorial on bow making will answer your questions. A bow is a bow.
I don't think there is a set of "Australian instructions" which will guarantee success first time, every time.
The "problem" is that bows use isn't an indigenous activity, so there is not the same traditional knowledge on selection of timbers and "styles" of bows which exist in other continents.
However if you are looking for a "bush bow", then you're really looking for what's readily available in your area, you're not trying to build a specific "English War Bow" or whatever ?
I think you should just go out, identify a timber, and build a bow. The process is the same if its a fine European timber, or a bush "stick".
I say identify the timber so you can see how well it works and perhaps try something the same or different next time.
The first bow will probably not work well, but by (googeling instructions, then) trying, you will learn a lot and the next bow will be better.
I do lots of projects which fail, but I always learn and then have the opportunity to improve next time. I can use my learning to investigate any "tricky" bits for next time.
... BY the way I've tried green blackwood wattle saplings, and have managed to make a bow, but not very good. Although the green saplings (approx 10 cm diameter, from memory) seemed to work, it quickly "fatigues".
My suspicion is a dried timber would be better, but thats more difficult to come by, and harder to work so will take longer .... but its all great fun and learning.
The better bows I've made have come from dried timbers, but take much longer and more effort to make (not surprising really) ! lol
Don't forget a bow isn't much use without a decent string and arrows. You could rough out a working bow fairly quickly from an appropriate branch or sapling. It wouldn't be a great bow, almost certainly take a set and not last all that long, but it would work.