Companies aren't supposed to charge excessive fees for using a credit card, but airlines have proved recalcitrant in reducing them despite fees that are clearly much higher than their own processing costs. Now Qantas has taken a tiny step towards cutting its fees, but there are only real savings to be had if you use a debit card.
Australian Business Traveller reports (and we've confirmed) that Qantas has reduced its per-booking credit card fee for domestic flights from $7.70 to $7. Excuse us if we don't do cartwheels over that relatively minor reduction. International flights still attract a $30 booking fee when using a credit card.
The news is somewhat better if you use a debit card; the fee has been reduced from $7.70 to $2.50 for domestic flights, and from $30 to $10 for international legs. If you use a debit card to pay for a flight that's less than seven days away, the fee is dropped entirely (although, as AusBT points out, your fare is likely to be more expensive in that case than if you had booked earlier and paid the fee).
The cheapest Qantas option continues to be paying via BPAY, which doesn't attract a fee at all if you book more than seven days ahead.