Carl's Jr now have an offers app, with their first batch including a free cheeseburger. You have to sign up to access the offers. There is nothing in the T&C's about buying anything to get the freebie, but YMMV. The free cheeseburger is not available at the Brisbane Airport store. Not sure what the normal price is.
Other offers include a Small Famous Star Combo for $4.95, $1 Small Soft Drink with unlimited refills and a $24.95 Family Deal which includes 1 Famous Star, 1 Hamburger, 1 Chicken Fillet Sandwich, 1 Original Angus Burger, 4 Small Drinks, 4 Small Fries, 2 Sundaes and 2 Cookies. All offers end Sunday February 9.