Green’s Dictionary of Slang

(Aus.) a felt hat.

1911		Critic (Adelaide) 18 Jan. 8/1: For I’m buying me a feltie / And a turn-down-collar shirt.
1912		Sport (Adelaide) 25 May 14/4: They Say [...] That Young ’un S, says he bought his felty while on the Ink (turn it up Reggie).
1938		Aus. Worker (Sydney) 16 Mar. 4/1: Feltie was quite, the smartest hat in the shop. He was perched on a brass stand in the middle of the window.