Green’s Dictionary of Slang

1. (Aus.) a pipe.

1895		Crowe Aus. Sl. Dict. 24: Dood, a pipe.
1902		Clipper (Hobart, Tas.) 9 Aug. 2/6: The ancient granny was a native of County Clare, Ireland, spent her latter days in praying and smoking a long doodee.
1918		Dandenong Advertiser (Vic.) 4 July 2/3: Smoking a clay ‘dood,’ and accompanied by a faithful canine chum, Mr Rook gave a wonderfully fine impresssion of a tramp’s meal.
1941		Baker Popular Dict. Aus. Sl.

2. (US) the penis.

1953

Randolph & Wilson Down in the Holler 101: Dood, which rhymes with rude, also designates the male organ.