I'm late getting to this, but a sad farewell to Yvonne Craig... she starred opposite the Bat, the King, and the Kirk (two Kirks, actually... James T., sure, but also Tommy Kirk in Mars Needs Women), and held her own every time. More importantly to my profession, she was probably the first and greatest Pop Culture Librarian of all, and she will be missed. Rest in peace, Ms. Craig, and thanks.
And to finally answer the musical question, whose baby was she?
No one's. Batgirl was no one's baby. Because her name wasn't baby, it was Barbara... Batgirl if you're nasty. End of discussion.