Ok, my thoughts ...no warranty, this is not advice etc.
Firstly, as OZ is where you intend to be, and you want to start investing now it makes sense to do it in Oz in AUD. Presumably you still have Oz bank accounts, TFN and mailing address, and someone to redirect your mail ?
As you will be earning less than 18k (investment return) ATO doesn't need you to do an annual return. So, get an account set up with Vanguard OZ, transfer $$ back to your Oz savings / transactional account and pay it out of that (Vanguard investments can be made by Bpay). As you save more, send it home and put it in to Vanguard fund of your choice.
Good luck!