My wife and I are living in Ohio, have been residents for 9 months and have a 14 month old child. If we divorce and she would get custody, could she ever move out of the state

Depends on what is negotiated in the divorce decree. If you are given joint custody with frequent visitation she would proably have to get court approval to move.

I have full custody of my youngest son and if I want to move out of state, I still need to get my ex's permission. If he says no, then I can go to the Judge and state my reasons I want to move. That is how my divorce decree states that issue.

Talk to your attorney. Sometimes the divorce decree uses the standard 'rule" but if you and your wife agree on something, it can be written in.