Wikipedia had this to say -
“Moll” derives from “Molly”, used as a euphemism for “whore” or “prostitute” and attested at least since 17th century England. It is also worth noting that “molly” is a term for a female cat, though it is much more rarely used than “tom” is for males.
Re: Moll as “Whore” — c.f. Daniel Defoe’s salacious novel “Moll Flanders”
IIRC, kittenclaws mentioned ecstasy upthread.
Molly is a slang name for the ecstasy drug.
KC, if I pinged you in error, apologies.