Find someone in AU who can send bitcoin directly to your wallet, while you pay him in cash. I don't see a better method than this to help you in securing your bank account to not be tracked.
I can't think of any ways except person to person transaction that will avoid you to provide personal data.
This is one of the best methods to keep your privacy since the transaction occurs only between you and the seller, although a bit risky since you need to have a face-to-face encounter and we never know who will be the one we are transacting to, using a DEX is another option but I wonder how one can transfer funds online without using a payment processor or a bank transaction? The P2P platform may not inquire about the KYC but the third-party payment app for fiat currency might be one to need the personal data.
In this case handing fiat directly to the seller is the best choice for privacy just like @asriloni stated.