Green’s Dictionary of Slang

(Aus.) of indiduals or objects (usu. clothing), unfashionable, old.

1903		Arena-Sun (Melbourne) 15 oct. 17/1: Amongst the gentlemen, there was the usual, if infrequent, bowler hat, brown boots and doddy coat, even, in one instance at least, a straw hat.
1911		Truth (Sydney) 9 July 10/4: Joseph Trappani, who was dolled up in great style, and who wore a doddy neck-tie, sported a chain, gold medal, etcetera., was the next witness.
1996		J. Byrell Lairs, Urgers & Coat-Tuggers 312: It seemed that every fat old Canterbury member’s doddy missus wanted to meet and congratulate the yobbo from the sticks.