Babcock's television appearances began in 1956. They included several episodes of the original series of "", although much of her work on the show consisted of uncredited voice roles. In 1968, she made her debut on the big screen in the Metro-Goldwyn-Mayer western "Day of the Evil Gun", followed by roles in the films "Heaven with a Gun", co-starring Glenn Ford, "Bang the Drum Slowly", "Chosen Survivors", "The Black Marble", "Back Roads", "The Lords of Discipline", and "That Was Then... This Is Now". From 1978 to 1982, she played the role of Liz Craig on the CBS soap opera "Dallas". Other notable films include "Heart of Dixie", "Happy Together", "Far and Away" and "Space Cowboys".