Gillespie was born in Montreal, Quebec, Canada. At age ten, she started singing lessons with Glen Raikes, and eleven took dance lessons with Burch Mann, founder of the American Folk Ballet Company. She auditioned for The Mickey Mouse Club in March 1955, was hired, and appeared on the program for all three seasons of its original run. She was the leading female singer and starred in the serial Corky and White Shadow during the first season. In the third season, she appeared in the serial, The New Adventures of Spin and Marty, with Tim Considine and David Stollery.