Woomeras sound like a bit more to make, but an atlatl is pretty easy. It’s pretty much a stick with a nub on the end. Not that too complicated. There are videos for it online. You can really make it as complicated as you want.
For the simplest type, you could try something like this:
https://m.youtube.com/watch?v=rrlr02YDr5AFor a basic carved atlatl, you could try this:
https://m.youtube.com/watch?v=Jyf-v5vGgkgThe darts are where it’s more complicated. You want the shaft to be pretty flexible or it won’t fly straight. You can find saplings or use dowels (splicing or connecting in some way). Going back to the flexibility, which is super important, a good dart might be around 6 ft long and 1/2 inch wide.
Here is a channel with a lot of helpful content for that stuff:
https://m.youtube.com/watch?v=Jyf-v5vGgkgIf you want to just buy stuff so you can have something to reference in the future, try ordering from Thunderbird Atlatl.