Are you playing a female character? I'm assuming no because then I wouldn't see how it could be a question if you were playing a girl.
If no and you are playing a male, then I'm pretty sure "baby" in "1950s Vegas lingo" can generally refer to a man or woman (depending on how you say it and it what context).
Male,and,yes I seem to have forgot the era...
What threw me is,I last played through as a female,where he said it....

Damm old age lingo!