It actually doesn't sound bad. The Aussie accent didn't particularly stand out or anything, so you shouldn't be worried about that. It sounds a little nasally in some parts, but for this genre, it could work. I'm not sure as I don't listen to R&B very much.
As for the falsetto parts at the end, you just need some practice. It doesn't sound like you fully transitioned into the falsetto voice which is why you couldn't reach it. There should be less constriction and straining.
If you're concerned about not sounding too R&B, you can always try rock. You can already play the guitar and it sounds like you can probably sing rock too.