Flight Centre, like most retailers whehether travel or otherwise, charge an additional fee nowdays for purchases through credit cards. It defrays their costs (read: time taen for them to get funds from cc provider), whereas obviously with cash, it costs them nothing to handle and payment if received straight away.
You have to decide whether to pay cash (assuming you have it) and lose any access to FF points; or put on a CC and pay the charge (however receive the FF points).
You have to weigh up the cost ($75) versus the FF points received from ANZ (you don't state how much your fares are, but on discount economy, perhaps a couple of thousand +). Now that would equate to 2 flights (say BNE/SYD/BNE) and with prices for those flights being $75+ (perhaps you'd be able to get them that cheap during sales).
It seems pretty much line-ball as to whether the additional cost is worth the points...your call.