Hi FF
Basically from what you have laid out as a
PR status, your income and debt will be subject to Australian taxation law, and yes it should operate as you have stated.
However it is always best to be safe and have a professional check for you, I can recommend Joff Martin ex Deloitte Touche : 07 3870 3840 (int 00 61 7 3870 3840)
Regards
Chris