Helen Parrish, the daughter of a stage actress, began her movie career at the age of 4 in 1927's Babe Comes Home, playing Babe Ruth's daughter! By her teens she was making regular appearances on screen often in B-movies. These include the Mystery of the 13th Guest (1943) and X Marks the Spot (1942) where she played one of the operators of the Telephone Jukebox i have blogged about before.
Her movie career ended in 1949 but she moved into TV and appeared on shows such as Leave it to beaver. Unfortunately her career, which surely could have continued for many years, was cut short by her death from cancer at the age of just 35.