jacques I don't think the false naivety is helpful.
It gives the idea of being older for one thing, of wanting that part of your body to be attractive.
Do you think any piercing is OK on a 13 year old then? A nipple piercing? Tongue?
She's not 'responsible for what boys think' but it is ridiculous to suggest that 13 year Olds having something that is associated with a much older girl or woman is not going to leave a certain impression.
The op asked the internet for opinions, I'm giving mine.