No, bunnies do not lay eggs. As placental mammals, rabbits develop embryos inside a uterus and, after a pregnancy lasting about 31 to 33 days, give birth to a litter of often 12 or more bunnies.
According to Discovery News, since ancient times, eggs and rabbits have been a symbol of fertility, while spring has been a symbol of rebirth. So even though rabbits don't lay eggs, the association of these symbols was almost natural. ... The Easter bunny and Easter eggs originated as pagan symbols of spring and rebirth.