You need to tell the child benefit agency that she is living with you and not her Mum , you can then claim her child benefit. Obviously her Mum will lose the benefit as it can't be payed twice.
Is her mum working ? if so she may be claiming family tax credit to which she is not entitled , once you are getting her child benefit you should be able to claim family tax credit as well if you or your partner if you have one, are working. As has been said the child can not claim anything as she is under 18, it has to be the parent or other adult she lives with (ie you)