If you bought it from pet shops which carries other breed, it may bring some back home and cause your daughter some rash. Call the buyer and say that your daughter having rash, you are thinking about returnning the dog in case you decide to give up the dog eventually.
And give the dog a bath gently, it may get rid of some stuff in the fur.
Do your research on the web, one thing is this kind of dog does not cause allergy by AKC unless it is not pure breed. Medication can get rid of allergy, but i bet you don't want to keep your daughter on drug for long time.