Where does the word "totty" come from?

The word "babe" in the US refers to a beautiful or handsome person with sex appeal. It is of course derived from the word "baby," which means infant. Similarly, in the UK, the word "totty" evolved from the word "tot," which means small child.

Two UK-focused dictionaries of slang point to a narrower (and less benign) reading of totty (or rather tottie) than is implied by equating the term with babe. From Tony Thorne, The Dictionary of Contemporary Slang (1990):

tottie, totty, totsie n British a girl or women in general, seen as potential sexual partners. The word meant prostitute or woman of easy virtue in the 19th century and is probably an affectionate diminutive of Dorothy. It is still a fairly common term all over Britain particularly among working class males and servicemen. [Example:] 'A nice little tottie.'

Interestingly, another diminutive of Dorothy, Doll, was a common slang term meaning "prostitute" in the late 1500s through the middle 1700s, as is reflected in a character named Doll Common, a prostitute who plays a significant role in Ben Jonson's The Alchemist (1610).

From Eric Partridge, A Dictionary of Slang and Unconventional English, eighth edition (1984):

Tottie; occ. Totty. ... 3. tottie, rarely totty. A high-class whore: from ca. 1880. Ex Dot, Dorothy, or ex dottie, -y a little child,: perhaps influenced by titty [defined as "a sister; a girl or young woman: Scots coll.," which Partridge says may represent a child's pronunciation of sister].—4. Hence, a girl, a young woman, esp. if of a compliant nature, but not a whore: R[oyal] N[avy]: C.20. 'That mad pusser. Gone native. Shacking up with a Japanese tottie somewhere' {John Winton, We Saw the Sea, 1960).

Partridge also has an entry for the allied expression Tottie fie:

Tottie (or -y) fie. A smart young woman given to 'throwing her weight about'; a prostitute or near prostitute with such tendencies: Londoners', esp. Cockneys': C.20. The fie is of exclamatory origin ('Oh my!') ... Hence, Tottie Fay (pronounced Fye), alternatively Tottie Hardbake, a female assuming a haughty air: derisive Cockney: since ca. 1890.

In any case, both of these sources ultimately trace tottie to the name Dorothy.