my thinking is that its her body, and in the great scheme of things its not that bad, (i would have felt quite differently had she asked for a tongue piercing for instance....on that i would say NO) Plus i absolutely do not want her to sneak off and get this done behind my back....not that i believe she would. She is well behaved and not a difficult teen by any stretch.
i had booked her into a tattoo/piercing parlour, but when i arrived there was a sign on the door saying they were closed today 
so, thought i would take the opportunity to find out what others think and ask those with pierced belly buttons if they regret it?
cheers