Green’s Dictionary of Slang

1. (US) of a man, to have sexual intercourse.

1890–1904		implied in go doodling
1930		Charlie Lincoln ‘Doodle Hole Blues’ 🎵 I knowed a little girl who was very very nice, / She got to doodle once and she want it twice.
c.1940		‘Joe E. Brown No. 8’ [comic strip] in B. Adelman Tijuana Bibles (1997) 106: This [i.e. sodomy] is the way we sailors doodle each other.
1959		W. Burroughs Naked Lunch (1968) 200: You know yourself all a Jew wants to do is doodle a Christian girl.

2. to masturbate.

1993

C. Hiaasen Strip Tease 27: He [...] sits at the back and doodles with himself while I’m dancing.