If my niece wants to move with her dad when can she without any court orders

Unfortunately for her, she cannot move to the other parent's home without the permission of her mom.  To accomplish her goal without mom's consent, your niece's Dad needs to bring a suit to modify the parent-child relationship and follow that through to obtain a court order that changes custody.  During that law suit, her Dad could ask that the court confer with your niece about which parent's home she prefers.  The court will consult with any child age 12 and older.  Without going to court she will need to wait until she is age 18.