My 3 1/2 year old grandson had the same thing, I treated it as a fungal infection, washing his face with a dilute Iodine solution daily. He has olive skin so the patches were noticable. After 1 week of using the Iodine solution, and a little time in the sun, the spots have now gone. This fungal condition is very common in children and some adults, children can get infected with it by contact with other children at pre-school or day care.
It wont hurt your daughter at all to wash her face with the dilute Iodine solution, and if her problem is this fungal infection you should see results pretty quickly. Its a good idea to wash her bedding and dry it in the sun, particularly pillow cases, as spores from the fungus can be trapped in the fabric.