Just make sure your rabbit has plenty of grass hay or timothy hay to help prevent problems due to the stress of moving. Also make sure to provide a constant supply of cool water. If your rabbit seems to be too warm (panting, etc.), you can put a plastic soda pop bottle that is filled with water and frozen in the cage for him to lean against. It would still be a good idea for him to have time outside. I don't think rabbits should be purely indoors. They were not meant to never have fresh air and run around on the grass. A harness and leash or a fenced in area with a top (and supervision) is a great way to let your rabbit get some outside time.