Lilian Fowler

Mayor 1937-1939,
Alderman various periods 1935 - 1948

Lilian Fowler was the first woman elected to any local council in New South Wales. She held office sporadically after that point (1935–37, 1938–40, 1941–44, 1948), but on 7 December 1937 became Australia's first female mayor, holding the mayoralty until 1939.

A detailed article on Lilian Fowler is available at Wikipedia.