A silly fellow, or noodle: see NOODLE. Also a child’s penis. Doodle doo, or Cock a doodle doo; a childish appellation for a cock, in imitation of its note when crowing.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Donkey * Doodle SackNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes