Jaques Ha, I got mine done at 16 and stopped wearing earrings at 17 after a not so fun spell in hospital. 20 years later, they haven't fully healed. You can still see the mark and feel the scar tissue.
op of course I don't know your DD, I think its kind of obvious when you ask a question on an anonymous forum that no one will answer with your specific child in mind. My opinion is that 6 yo do not have the capacity to make truly independent decisions that will affect them permanently and also potentially affect their health. I think that is specifically WHY guardianship of children's health and bodies resides with parents at that age.
It isn't so much that nothing you have posted has changed my mind on that regarding your actual DD, but that basically everything you have said about her child's reasons for wanting this proves this point in spades.
She wants it done to 'look cool like her Dad', as no fully mature personality said EVER.
My 6 yo DD is currently copying my hairstyle (such as it is) and wanting matching clothing to me. I'm pretty sure she won't be doing that when she 8 yo, let alone 18.
But if your DH wants a mini me then yeah, go right ahead, personally I'm finding it cringy and can't wait for the phase to end.