All had tiny sleepers, not studs. They can't get caught and if they are pulled, the earring just opens and falls out.
That's not true, they can tear if they are caught, especially in the early stages. It's just easier than removing first studs!
OP, please bear in mind you would be taking a risk until your baby has had all her DTP vaccines (which includes tetanus).
Don't forget that some people simply cannot sustain ear piercings because of allergic reactions, even to gold.
I'm a fan of pierced ears, have had them done herself. But I would never have decided for my own DD to have them done. She went through a stage of feeling like she "should" have them done around 8 years old when many of her friends did. I asked her to wait, and promised her that if she still wanted to I'd be happy to arrange it at the start of her summer holiday before secondary school.
That's come and gone and she hasn't bothered. There's plenty of other jewellery to wear! Ask yourself whether you have the right to decide this for her, or whether it would be better to let her make a personal decision about what she wants done to her own body.