J.G.
First- don't use peroxide. It kills off the new cells that are growing and can cause scarring.
Second, If you have allgergies she probably does too, but not necessaraly to the same things. The suggestion for sugical steel or titanium is a good one, also if you trust her- 24k gold (my mom is allegic to nickel which is used as a filler in most jewelry- it's 24k or platnum for her)
Hoops this early in the healing process will cause the hole to heal curved which can be painful if she switches to straight posts later.
She is old enought to learn to clean them herself when she is at her fathers house, if she complains tell her her other choice is to take them out completely and let them heal (which might not be a bad choice anyway)
I got my first holes when I was five, two of my daughter before they were two (young enough to forget about them and let the heal) I have had a few percings that wouldn't heal, and one that I had to let close up after 5 years because of a sudden sensitivity to the jewelry that had been in it the whole time.