V.W.
I would take her to the doctor and get an exam. Peeling skin on hands and feet can be indicators of underlying conditions. But they wouldn't typically be the ONLY symptoms. Your doctor would know what other symptoms to be aware of or ask about. It could be as simple as psoriasis/dermititis due to some sort of allergy (soap, or something in your carpets/floors even), or a food sensitivity, or it could be indicative of something more serious. Has your daughter had a fever at all in recent weeks? It could just be a virus. Or it could be more serious, like Kawasaki's.
A doctor can ask the correct questions and examine your child to give you a diagnosis..... we can't do that on this site.
But peeling skin on palms and feet is not just a "normal" thing, if you have no known explanation for it. Get a diagnosis from her pedi.