Are your birds in a cage, or do they fly around? I don't have a bunny, so I'm not sure, but I think either way the birds will be fine.

As for bunny proofing (I have to do this w/ my guinea pigs too ) You have to get down a bunny level and check for stuff that can be chewed. Electrical cords are dangerous! I cought my piggy chewing on one once - luckly I saw her in time and pulled her away. You can tape them down to the floor with duct tape if you have to, or get them out of reach. And also check out small spaces, like under a dresser, where a bunny could get stuck. And keep your room clean! lol

Good luck with your new bunny! ^_^