Thanks for sending your question through, Bunny. The short answer is no but they do have the option of wearing one.
The traditional outfit of the Speaker of the House of Representatives included a black academic gown, a jacket, a jabot (lace collar) or white bow tie, a full wig and court shoes. It is the Speaker’s choice whether they wish to wear all, some or none of the traditional outfit.
In recent years some Speakers have chosen to wear business attire. Between 2011 and 2013 Speaker Peter Slipper wore elements of the traditional outfit including the gown, jacket and bow tie.
Sir Billy Snedden (Speaker from 1976 to 1983) was the last Speaker to wear the full ceremonial outfit, including the wig. The Speaker's wig has not been worn since the Australian Parliament moved to the new Parliament House in 1988.