I'm unsure about the history of most worlds, including yours. So I am basing it purely on my own. As Christianity spread over Europe, it took on aspects of whatever religion was there before. Various dieties became saints, holidays changed dates to match a festival or holy day already being celebrated, and symbols of old mythological beings were transferred over. Rabbits, along with chicks, ducks, and lambs, were likely symbols of some of fertility god or goddess with a feast day around the same time as Easter. The symbols just became associated with the new holiday.
Along with candy and toy rabbits, real ones are sometimes given to kids as gifts on Easter, which is why I'm expecting to be suddenly flooded witb them at work.