No no.
From a professional stand-point too.
I do think it's a bit too sexual a piercing for someone of that age, but then I don't think it is right to be imposing sexist ways of thinking onto a child by saying it's trashy for a girl to wear a certain type of piercing. I don't think that's the issue anyway, it's more about maturity, risks and the child's ability to make a mature decision.
Age isn't a factor as much as responsibility.
At 14 years old a person can make their own choice about body modification, but as a parent it's down to you to determine if they are making a choice or if they're just following a fad. Piercings should be treat the same way as tattoos, it's something that may remain for the rest of their lives.
At 14 a parents needs to give consent for the piercing - anywhere that pierces a 14 year old without the parent should NOT be trusted!
Piercing should be taken as seriously as minor surgery If anyone goes to a piercer who is not trained and hygienic then that risks general infection, scaring, body shock, TSS, Hepatitis and HIV. I see many parents just come along to the studio with their kids, but ask no questions at all to ensure safety, which I just find to be shameful. The fact that parents allow their children, even babies, to have ears or other areas pierced with piercing guns implies that many parents are very much ignorant of the risks.
Younger people need to be mature enough to take care of it correctly - often we find they don't clean it properly or remove the piercing, they're especially bad for removing the piercing when infected which is the worst thing a person can do with a piercing. It's a lot more common for younger people to unintentionally pull the piercing out, ripping the skin in the process. You as a parent can check it for them, but then that would imply the 14 year old isn't mature enough for the piercing.