Fisher made her debut in the 1985 crime drama "Stick", starring Burt Reynolds, Candice Bergen, George Segal, and Charles Durning. She then starred as Daphne Ziegler in the 1986 comedy "Pretty Smart". In 1987, Fisher appeared in the television movie "Strange Voices", opposite Valerie Harper. The following year, she landed a role in the TV movie "Bring Me the Head of Dobie Gillis", also starring her mother as well as Dwayne Hickman and Bob Denver. In 1989, Fisher appeared in two movies, "Hollywood Chaos" and "", followed by roles in the 1990 comedy, "Book of Love" and "Arizona Dream" starring Johnny Depp, Jerry Lewis, and Faye Dunaway.