Hii , Welcome To HCM & Thanks For Asking Your Query Here Dark circles under the eyes in children are not usually from lack of sleep or troubled sleep , however it does not necessarily mean they your Daughter have poor health or lack vitamins or nutritions in Children it is most likely caused by nasal congestion , If the nose is blocked, the veins around the eyes get larger and darker. Nasal congestion can be caused by hay fever, sinus infections, colds or allergies. It can also be caused by large adenoids, which cause your child to breathe through his mouth more than his nose. Nasal congestion can also be a result of enlarged tonsils. i would strongly suggest you to see a Pediatric , he will examine her thoroughly and will rule out any underlying medical condition I hope it help Thanks & Get well Soon