Green’s Dictionary of Slang

(US) the penis.

1925		E. Field ‘A French Crisis’ in Facetiae Americana 20: With dornicks so proficient that when they cease to spout [etc.].
1953		in Randolph & Legman Ozark Folksongs and Folklore (1992) II 677: His dooflicker’s long and his dornick is tall.