Edie is part of the Evie-Ellie et al family of cute and friendly short forms that sometimes stand on its own. Briefly popular in the 1960's, it could well be due for rediscovery.
Several Ediths have chosen to be known by this pet form, including socialite and Andy Warhol superstar Edie Sedgwick, actress Edie Falco, singer Edie Brickell and the Jacqueline Bouvier Kennedy relatives called Big and Little Edie in the iconic documentary Grey Gardens. Edie Britt was the character portrayed by Nicolette Sheridan in Desperate Housewives.
British actress Samantha Morton chose Edie for her daughter.