What is the process for getting child custody before I need to relocate to another state

Your best bet is to get your husband to consent to the move. If he doesn't you may file for custody in Family Court and seek the court's permission to move. If you move without the court's permission, and the father files seeking custody, the court may find that you have moved to prevent the father from seeing his child and direct you to return or direct that there be a change of custody to your husband. Relocation cases are very problematic and if you are not able to come to an understanding with your husband, that you reduce to writing, I would strongly recommend that you seek the advice of a good family law/divorce lawyer on this issue.