If I want to move out of state and my ex-husband and I share joint legal but he has primary, do I have to go through the courts?

If you and your husband share joint legal custody of a child and you want to move out of state, then the answer to your question will depend on your orders.  Courts sometimes place movement restrictions on parents who have primary custody of the child, but not very often on the non-custodial parent.  Instead, they usually have a set of orders built in to the visitation schedule for when one parent moves farther away.   You do not have to go through the courts to get permission to move unless you have an unusual order that restricts your movement.  If you do have a restriction, then you should get the order modified to avoid any contempt or enforcement actions. 

There is nothing prohibiitng you from moving out of state if that is what you wish to do. However, given the current custody order that you have written about for you to be able to legally take your minor child with you on the move you must file a petition with the court seeking what you want, serve the petition on the child's father and have a hearing on it before the court where the court makes a final decision as to your request.