Well, if Alpert is immortal, why not bunny no. 8?
What a mean pet owner Ben is, if so. lol.

Would it not, then, be an unusually long-lived bunny? Can the bunny stay forever young? Do rabbits have better luck breeding on the Island than humans seem to?

There's something with the white rabbits don't you think?
Locke told Jack to follow his white rabbit in the "The White Rabbit" before he finds the cave with the water, Adam and Eve and his dead father's empty coffin (Dead? we never saw the body in the island yet, did we?). Then, we saw Ben´s white rabbit in TMBTC, before Ben foinds Richard and the whispers for the first time. We don't know if it is the same rabbit Ben operated in the Hydra (sholud be the same one, rabbit don´t live that long). And, if I remember well, we saw a white rabbit's leg in the key holder with Dharma's Van in "Tricia Tanaka is Dead" (now we know it was Ben's father's vehicle with his dead body inside)...
Is something behind these white rabbits?
What do you guys think?

Well rabbits have been long associated with fertility.

Well rabbits have been long associated with fertility.

Yes, and this is a reference to Alice in wonderland too.