Australia card purchase never arrived: can I ask for a chargeback?

Potentially. ACCC says a card provider may be able to reverse a charge in some situations, including where a credit-card purchase was not delivered. Time limits can apply, so contact the card provider promptly and keep the order, payment, seller messages and non-delivery evidence. Official source: ACCC. Guide: https://getinstantlaw.com/chargebacks-payment-disputes