I am not saying your daughter will but.... I went to high school with kids that had some one pierce their navals at their house because their parents wouldn't sign off and some ended up with some pretty bad issues because of their choice. I saw some gross infections and their was a rumor one girl got Hepatitis.
I don't have kids but I would think putting aside your dislike of it and letting her get one may be the safest thing for her. Tell her you don't want to see her playing with it (bizarre fascination of my friends with them) and you don't want to see it. Just from experience, I would consent so it is done at a reputable place. A naval ring is pretty darn tame IMHO, of course I was raised in Austin and we pride ourselves on "Keeping Austin Weird".
Amanda
2011 Specialized Epic Comp 29er | Specialized Phenom | "Marie Laveau"
2007 Cannondale Synapse Carbon Road | Selle Italia Lady Gel Flow | "Miranda"
You don't have to be great to get started, but you do have to get started to be great. -Lee J. Colan