The bunny has nothing to do with Easter.
Most societies depend on the fertility of their fields for food. They depend on the fertility of their farm animals not just for food, but also for the muscle power to pull the plow and the grindstone, and they depend on the fertility of their own bodies to produce sons who can labor in the fields and daughters who can fetch dowries. So natural religions generally center on fertility—of everything in the field, the barn, and the marriage bed. In a fertility religion, the greatest good is marriage and bearing children. This can lead to gross immorality, as happened in the middle east in ancient times, because infertile people sought a remedy in the arms of the priests and priestesses—and it became a religious act, because by having union with the priest or priestess, they were communing with the pagan fertility god. The Old and New Testament writers constantly condemned this, because for them it was a contemporaneous practice. Isaiah 56:3-5 even prophesies of a future time in which the infertile would no longer be outcasts.
In the British Isles and Germany, the spring fertility festival involved eggs and bunnies, because they are natural symbols of fertility, and it also involved worshipping trees. The Christian missionaries who brought Christianity to the British Isles and to Germany suffered quite a lot of grief at the hands of our ancestors when they chopped down the sacred trees to demonstrate that they weren’t gods. Since the people did not actually worship the bunnies and eggs, the missionaries figured they could just Christianize them. So the custom began of painting Christian art on eggshells and they just tolerated the bunnies. I guess they would be greatly saddened if they could see that the eggs and the bunnies once again overshadow the cross.
It is common for missionaries to incorporate existing traditions into Christianity, wherever it’s possible to do so without compromising the faith, because it isn’t practical or necessary to abolish a native culture, along with all its festivals and folkways, just to introduce Christianity. For this reason, Christmas is called ‘Yule’ in Nordic countries—‘Yule’ is the name of the winter-solstice holiday that Christmas supplanted. In the same way, English-speaking Christians retain the name ‘Easter’ for the holy day that is called Passover by Greek-speaking Christians.