Is it permissible for a girl to undergo a virginity test if she is accused of being in an illicit relationship and of harassing a doctor who harassed her?

It is not permissible to expose the grave awrah (private parts) except out of necessity. If examination is the only way to prove innocence from indecency, then there is no harm in it, because it is a compelling need that takes the place of necessity, which permits what is otherwise forbidden. This examination must be performed by a woman.