My 4 yo daughter has underarm body odor like an adult would have. she shows no other abnormal signs-no hair, breast development. is this a problem?

This does happen: with children sometimes without any underlying reason or problem. However, I would recommend discussing this with her pediatrician, and having her examined by them also. They may suggest some laboratory testing to rule out a metabolic or endocrine problem, but they may also determine that it is not a problem and allow you to use a basic deodorant only product.