Carter made her Broadway debut in the 1971 rock opera "Soon", which closed after three performances. She was the Music Director for the 1974 Westbeth Playwrights Feminist Collective's production of "What Time of Night It Is". Carter appeared alongside Bette Davis in the 1974 stage musical "Miss Moffat", based on Davis' earlier film "The Corn Is Green". The show closed before making it to Broadway. She broke into stardom in the musical "Ain't Misbehavin", for which she won a Tony Award in 1978. She won an Emmy for the same role in a televised performance in 1982.