You don't really need to plant anything. A loose brush pile is great for providing the cover small animals need. The cut up holly bush may be just the thing to build it with.

Of course, a brush pile doesn't fit everyone's definition of landscaping, but the bunnies will love it.

Think if it were me & you can I'd just trim it up good rather than remove it so you're little critters won't be too disturbed.
Good luck with whatever you decide to do... :-)

I'm with Dreamweaver, it's pretty late to be moving somethings home. How long before you expect freezing temps? Lots of little critters already have established winter dwellings. If you have bunnies you probably have chipmunks too, they have been stashing food for quite some time now.Can you just trim it so you can live with it for now, then consider removing it after the babies are gone next summer?
Lisa

I think maybe I wasn't clear when I said what I wanted to do!! I wasn't thinking at all about doing anything with this bush right now because winter is coming and I know that the animals have gotten ready to winter there. I guess I was just thinking ahead for next year and how I would go about getting rid of this bush while still providing an environment for the animals that usually make it their homes. Thanks everyone for your help.

Can't you trim it in the spring? Hollies provide food and cover for many animals. Robins in the north east live off holly berries in the winter.

Rabbits around here seem to thrive in the medium height juniper shrubs.