I'm Rh negative and the baby's father is Rh positive so what do we do?

Only if you are Rh+. Rh positive mothers having rh+ babies-no problem! rh negative mothers with a rh+ baby especially the first and subsequent pregnancies will require Rhogam injection post delivery to prevent future rh disease issues and baby losses.
Be a happy family. Your physician knows how to treat you with today's medicines to keep you from becoming sensitized to the Rh antigen that Daddy and Baby share.