Green’s Dictionary of Slang

doodle-sack n.²

the vagina [doodle n.² (1)].

c.1786		Grose Classical Dict. of the Vulgar Tongue ms. additions .
1788, 1796		Grose Classical Dict. of the Vulgar Tongue (2nd, 3rd edn).
1811		Lex. Balatronicum.
1890–1904		Farmer & Henley Sl. and Its Analogues.