A letter her mother wrote to producer Carlton E. Morse got her a part on One Man’s Family playing Penelope Barber Lacey (Penny) when she was only 7 years old, a role she would continue almost until the series left the air in 1959. Numerous radio jobs followed including Suspense, Lux Radio Theater, the Lady Esther Screen Guild Theater, Cisco Kid, Family Theater, The Great Gildersleeve, The Life of Riley, The Halls of Ivy and Cavalcade of America. On Baby Snooks, Anne was frequently heard as Pamela Richardson, the snobbish daughter of the local banker. Her signature role began in 1946 when she began playing the younger daughter of Phil Harris and Alice Faye on the popular Fitch Bandwagon (later known as the Phil Harris and Alice Faye Show which ran on NBC from 1946-1954.