Please do not take a rabbit from the wild. It will not do well in captivity and it is usually illegal to take animals from the wild without a permit. Plus, it will be terribly skittish, and possibly have diseases, worms, etc (these could either kill the rabbit, or be transmitted to you or your other pets). If it is not moving much, it is likely sick or scared to death (a healthy rabbit simply wouldn't let you go and pick it up, especially considering you are bigger and more terrifying than most predators). If you want a rabbit, please consider adopting a domestic rabbit or buying one from a reputable breeder. They make much better pets. I would find your local wildlife rehab center and consider taking the rabbit there so they can examine it and then properly release it.