Green’s Dictionary of Slang

(Aus.) a yarn, a story, thus spin a dit, to tell or swap yarns.

1962		J. Wynnum Tar Dust 48: He looked forward to a snort up on the hill and the opportunity it offered to swop ‘dits’ with his offsider in the cruiser.
1962		J. Wynnum Tar Dust 22: Kate coughed with self embarrassment, realising that Toggle might spin the odd dit about him.