The Lady Is Willing (1942)

Bold, eccentric Broadway performer Liza Madden befuddles her handlers by coming home with a baby she picked up on the street. She wants to keep the baby but has to find a husband to make adoption viable. Why not her new obstetrician Dr. McBain? She offers him help with his research on rabbits in exchange for marriage - and he accepts. The mismatched pair begin a marriage of convenience...