We have square linked to our NAB account and am offered instant transfers (although we don't use them). It appears that any bank that supports the NPP (payid) should work.
More details here:
https://squareup.com/help/au/en/article/5405-set-up-and-manage-instant-deposits
The FAQ states that most AU banks are supported but not credit/debit cards but also states they can't determine whether it will work for instant transfers until it's actually linked..
https://squareup.com/help/au/en/article/5440-deposit-options-faqs
If you have an existing bank account, perhaps link it and try.
Bruce
