Green’s Dictionary of Slang

(Aus.) the head.

1853		Empire (Sydney) 21 Jan. 2/6: Mr. Horne made chase, but it being a dark night, [...] they succeeded in making their escape, although Mr. Horne fired his pistol at them, and so close as to go through the wool of Wickaty Wee’s ‘cobbera’ .
1870		Sydney Mail 16 Apr. 9/6: He ain’t so young as he was thirty years ago, and the top of his head is as smooth and as shiny as a Charney [?] alley, though he does try to take the down off by brushing the hair over it from each side of his nob, but lor, it don’t cover it no how, and ain’t even enough to keep the mosquitoes off his old cobbera.