Wild baby rabbit?

My brother-in-law was mowing his lawn and almost ran over this little rabbit, he picked it up and brought it to me for my daughter to keep as a pet. I accepted it, but after watching it be scared almost to death I've decided it would be much more humane to release it again. It was found alone and not in a burrow. It doesn't have a white blaze on it's head and I've heard that means it's old enough to make it on it's own. My problem is that I don't know where the best place to release it would be. We live out in the country but there are 14 dogs and at least 2 cats roaming the nearby area at any given time. Would it be better to let her go where she is familiar and let her risk it with the dogs, or relocate her somewhere there are fewer dogs but not familiar to her? She seems healthy although she will barely move, but I think that's just fear. My mother thinks I should keep her til she's older and then release her so that's also an option.