Australia's domestic airlines are:
Qantas, which is part of Oneworld.
Virgin Australia, no alliance but partners include Delta.
Jetstar, LCC arm of Qantas
Tiger, LCC

You can get Australian credit cards that earn with either QF or Virgin.
Grocery shopping mainly is QF points earning.

I guess it depends on how long you are in Australia for, and how many domestic flights you will be taking.

But I would recommend looking first at AAdvantage, perhaps with a challenge to get status, and then QFF.