Moore was born in Brooklyn and grew up in California. She started off with a role on the "happy Hotpoint" commercial, in which she would dance around on the kitchen appliances. Her first regular television role was on the show Richard Diamond, Private Detective; however, in that show, only her legs were ever shown. Her first important television role in which gained wide recognition was as Laura Petrie in The Dick Van Dyke Show.
In addition to her acting work, Moore is International Chairman of the Juvenile Diabetes Research Foundation International. In this role, she has used her fame to help raise funds and raise awareness of diabetes mellitus type 1. Moore suffers from this illness.