There can not be a debate on ear piercing as it is cultural.
African, middle eastern, people from the Islands pierce girls ears as babies while Europeans usually let their girls decide for themselves when they want it done, usually as young adults.
If you go to any nice jewlry store they will do it for free and you only have to pay for the earrings.
I did my daughter's ears at the same age.
Make sure you buy 18k earrings with the screw in back.
14k Gold and under is mixed with nickle, which is why it so cheap and can cause an allergic reaction.
I took my daughter in at three months, while she was sleeping. They use a gun and it takes not even a half of second. She opened her eyes and than closed them. They clean the gun and ear with anticeptic before they begin.
The gun puts the earring in.
There will be no infection or pain.
There is no bone in the ear lobe.
She will feel the earring, but with the screw back, she will not be able to get it off.
And than she will no longer notice them.
Good luck and I bet she's going to look so cute.
Get her birthstones!
And take pictures!