Probably "reaching" more than a bit; however -- rabbits, though now reckoned as in the order Lagomorphia, used to be considered rodents; and the orders are closely related. "Rabbit" in German: Kaeninchen. If you're extremely fond of your pet, I suppose you might construct a mini-town for it to live in: so, Kennington (London Underground) ?
It isn't Kennington, nor is the station in London at all.
But you are along the right lines.
Think of a particular rodent, and what you might call somewhere that rodent would live in.