I believe (and could be wrong) that the belly piercing will close up if you take the stud out. I don't think it is a great idea at all, and at the age of the girl in question, the parent can just say no as they like.
HOWEVER, here is my PSA against piercing: I had multiple piercings in my ears (8 in the left, three in the right) in high school-college, but ended up having to take them all out because of a reaction I developed to metals. Even now, I cannot wear anything in my ears, even gold, and all necklaces, bracelets, etc. have to be 14K gold or sterling silver, or I grow a rash across my skin, where-ever the metal has touched. My ear piercings were infected sometimes, but a septic ear is easier to treat than a septic tummy ring. IF you get pierced, make sure it is by a liscensed place, and follow the instructions for aftercare.
One thing I always say: the piercings I had were temporary--some things, like tatoos, or "body modifications," are forever!