c. 1600, Dolly, a fem. nickname, extended form of Doll, short for Dorothy (see doll (n.)). In 17c. slang "a female pet or favorite." Modern slang sense of "young, attractive woman" is from 1906.
From 1790 as "a child's doll;" applied from 1792 to any contrivance fancied to resemble a dolly in some sense, especially "a small platform on rollers" (1901). Doesn't look like one to me, either, but that's what they say. Compare jack, jenny, jimmy, etc., generic proper names applied to various mechanical contrivances.