To my surprise I discovered you can still by new Ansett buttons from Flarose Pty Ltd. Here are my three new buttons.
This basic design was used by Holyman Airways and the airway that took it over, Australian National Airways. ANA was sold to Ansett in 1957, becoming Ansett-ANA, renamed in 1968 as Ansett Airlines of Australia.
See also http://www.austbuttonhistory.com/uniform-buttons-2/companies-and-clubs-including-merchantile-marine/
The button below has an RAAF type eagle on top of a map of Australia. The button was made by the Dowd Corporation who supplied the Ansett Flight Crew uniforms. The logo was also used on the pilot cap badge.