Green’s Dictionary of Slang

1. (Aus.) exhausted, tired out.

1917		‘Henry Handel Richardson’ Aus. Felix (1971) 145: ‘Lor, Polly! your bit of a kitchen . . . in this weather . . . I’m fair dished,’ And the good woman mopped her streaming face.
1984		Partridge DSUE (8th edn) 314/2: since ca. 1930.

2. see dished adj. (1)