Green’s Dictionary of Slang

(Irish) the penis.

c.1785

‘The New Dhooraling’ in A. Carpenter Verse in Eng. in 18C Ireland (1998) 400: Too long the Doodeen was the toast / Altho’ no more than an empty boast, / Sweet Dhoora now is the pleasing toy / Diverts the girls tho’ ever so coy.