Bunnies do not lay eggs. The Christian holiday of Easter has some customs associating rabbits with eggs, but rabbits actually give birth to live young. Rabbits are mammals, and only three species of mammals are capable of laying eggs.
None of the living species of egg-laying mammals are closely related to rabbits. Rabbits do have specialized reproductive cells called eggs, but these cells are very tiny and, when fertilized, do not develop into an external hard-shelled egg containing an embryo. Instead, the fertilized egg develops into a zygote that attaches to the rabbit's uterus and develops into a baby rabbit. The process is very similar to human pregnancy and child birth.
The traditional Easter association of rabbits with eggs comes from ancient pagan celebrations held in the spring that used both rabbits and eggs as symbols of fertility. When certain parts of Europe were converted to Christianity, these older symbols merged with the celebration of Easter, because Easter was also held in the spring.