Does a parent of a 13 year old girl have the right to find out what the child has discussed with a counselor?

The doctor-patient privilege is a form of a right to privacy that is derived from the U.S. constitution. This rule would apply generally to the counselor/patient relationship as well.  The individual states each have in place their own set of rules regarding the right to privacy.  Some states may deem it necessary for the patient to be entitled to the privilege even to the exclusion of the minor patient's parents.  However, it is also the case in some states that doctors (or counselors) will be given some latitude to discuss with the child's parents the scope of the conversation in counseling.

This type of right to privacy is, at its roots, derived more from ethics than it is from the law.  Thus, if the circumstances would call for disclosure by the counselor, then such disclosure to the parents (or otherwise) would likely be permissible.  For instance, if the counselor had knowledge that the child was subject to forthcoming danger or legal trouble, this kind of information can often be disclosed to protect the child or to protect others.

But whether the counselor may divulge the substance of the conversation with the patient is going to be a rule of state law.