Can I move with my unborn child if the father is stationed out of state?

You appear to be a pregnant unwed mother. As you are not married, the putative father has neither custody nor visitation rights until either he, you or the state, if you are receiving state assistance, takes the putative father to court and establish him as the legal father. He can seek custody or visitation if he elects, as part of a paternity proceeding, but if he does not, he will simply have a financial obligation to support his child. Not every person, male or female, who helps create a child, stands up to be counted. So, at this time, unless the state or you or he already has an active action, you can move, or not, as you elect. If there is an action in place, and if you do not have counsel, reconsider that choice. If you do have counsel, ignore everything I just wrote and go see your counsel. He or she is in the best position to advise you.