Cartwright was born in Bristol and grew up in Los Angeles, having emigrated to America shortly after the birth of her younger sister, actress Angela Cartwright. Her career as a child actress began in 1958 with a role in In Love and War. Among her early appearances were repeated roles in the television series Leave It to Beaver (as Beaver's classmates Violet Rutherford and, later, Peggy MacIntosh) and episodes of One Step Beyond "The Haunting" (1960) and The Twilight Zone "I Sing the Body Electric" (1962). She guest starred twice in 1963 in NBC's medical drama about psychiatry, The Eleventh Hour, in the episodes "The Silence of Good Men" and "My Name is Judith, I'm Lost, You See. " Cartwright appeared in the films The Children's Hour (1961) and Alfred Hitchcock's The Birds (1963), which were both highly successful. In The Birds, she was cast along with her TV father from Leave It To Beaver, Richard Deacon, although the two were not on screen together. She played daughter Jemima Boone in the first two seasons of NBC's Daniel Boone from 1964 until 1966, with co-stars Fess Parker, Patricia Blair, Darby Hinton, Ed Ames, and Dallas McKennon. She won a regional Emmy for the 1964 TV movie Tell Me Not in Mournful Numbers.