According to Google, the phrases "Do bunnies lay eggs" AND "Do rabbits lay eggs" each receive between 1,000 and 10,000 average monthly searches! What does that say? If they're asking, they really don't know.
By the way, the answer is NO.
Booboo the baby white Holland Lop bunny, the cutest bunny rabbit ever, pretends to be the Easter Bunny rabbit and lays some Easter eggs in a basket . . .