She is known for her performances in the Broadway revival of Peter Pan, the sitcom The Hogan Family, and the Disney films The Million Dollar Duck and The Cat from Outer Space.

Duncan made her feature-film debut co-starring with Dean Jones in the Walt Disney family comedy The Million Dollar Duck.

She was then cast as Amy Cooper in the Paramount film version of Star Spangled Girl, based on the Broadway play by Neil Simon.

Critics dismissed the show but praised Duncan, especially TV Guide columnist Cleveland Amory, who described her as "a wonderful comedienne.

"[This quote needs a citation] Shortly after the premiere of Funny Face, Duncan underwent surgery to remove a benign brain tumor behind her left optic nerve.

Her recovery from the operation was rapid, but CBS suspended production on Funny Face until the following year after the 12th installment had been filmed; the original series pilot served as the 13th (and final) episode.

Duncan was nominated for an Emmy Award for Outstanding Continued Performance by an Actress in a Leading Role in a Comedy Series.

In 1976, Duncan played the title role in a television musical adaptation of Pinocchio that featured Danny Kaye as Geppetto and Flip Wilson as the Fox.

In 1976, she guest-starred on The Six Million Dollar Man and The Bionic Woman playing the role of Gillian in "The Return of Bigfoot" episodes.

In 1978, Duncan starred in Disney's The Cat from Outer Space along with Ken Berry, Harry Morgan and Roddy McDowall.

at Radio City Music Hall and provided voice work for the My Little Pony television special Rescue at Midnight Castle as Firefly and Applejack.

In April 2009, she performed the lead role in the play Driving Miss Daisy at Casa Mañana Theatre in Fort Worth, Texas.

This marriage also failed, according to Duncan, because of the demands of her 1978 nightclub act and her refusal to remain at home to be a good "doctor's wife.