Green’s Dictionary of Slang

(Aus.) a (peaked) cap or hat.

1895		Crowe Aus. Sl. Dict. 23: Decker, a hat.
1901		Bulletin (Sydney) 5 Jan. 25/1: A new sailor-hat was trotted out by an enterprising firm last week, specially for the Sydney trip. This latest joy in straw-deckers has, stowed cosily in the crown, a boná-fide fringe to be let down or taken up as one pleases.
1908		Bulletin (Sydney) 27 Aug. 14/4: This ‘decker’ hanging round my nose / The product of an Ode to Rose; / The collar, tie and underpants / Are still an Editor’s advance.
1914		Sport (Adelaide) 4/5: Sid W and Fred D have joined the straw-decker gang.
1922		Gippsland Times (Vic.) 2 Nov. 5/2: Aw! run away, yer silly dope, / Afore I spoils yer decker.
1951		D. Stivens Jimmy Brockett 58: I was wearing a new straw decker which set off my grey suit. Top hats and bowler hats are all right in their way, but a bit too old and formal for me.