Based on your position as her parent, you alone can make the judgement call on whether you can trust her to have this done and remain a responsible teenager. She's in high school now, and the burden of responsibility is starting to sink in. All children are different, maturity levels fluctuate quite extremely between individual to individual at that age -- it's really down to you to answer that.
For what it's worth, I think piercing is more of a social taboo as opposed to any kind of corrupting influence. If you think a belly button piercing is anywhere close to being the reasons why this generation are "over sexualised" then I think you're barking up the wrong tree.
That said, as someone posted prior -- you might want to ensure she's aware of the medical aspects.
Yes i fully believe the onset of the premature sexulisation of children was brought about entirely because of belly button piercings. The earth is flat right?