Can 12 year girl can use NY BAE face serum on her face without any skin reaction?

For a skin so young, I'd suggest you to not ruin it by the wrath of harmful chemical based products.  II'm not sure if it will cause a reaction instantly, but I'm certain that if the skin starts absorbing chemicals at such a tender age, it'll show up in various forms (Acne, loose skin, pigmentation, dark spots, wrinkles, pores, etc) in the future.  I'd rather suggest you to adopt a natural, toxic free skin care routine. Check out this Ibbani Naturals Rejuvenating beauty serum.