Why is it a Bunny?

On the way to the shop to grab the newspaper this morning I came across a rabbit.
He or she was just minding its own business on the side of the pavement in front of an area of scrub and trees. It was pretty tame, or at least not jumpy at all, and I stood there for a few minutes watching it.
As I went on my way I wondered why is a rabbit, or bunny, the symbol of Easter?
And why do they deliver eggs? Rabbits can't lay eggs, chickens do. So why isn't it the Easter Chook?
I consulted the all knowing Wikipedia for some answers.
Apparently bringing eggs is a tradition that began in Germany in the 1600s. Because Easter falls in the spring in the northern hemisphere the rabbit, or hare, became a symbol due to its prolific breeding habits. Just like at Christmas, apparently only good children received eggs at Easter.
Of course these practices have become commercialised to the point that Easter Eggs are available for purchase shortly after Christmas.
I'm not entirely sure I'm satisfied with the origin of the Easter Bunny and it's actually quite disturbing that a rabbit delivers eggs for you to eat.
It's a good thing that they're generally pretty cute creatures - but, still, it's a bit icky.

Oh, by the way this was my 800th post. Can't believe it.