There are several issues with your planned course of action. Under the Uniform Child Custody Jurisdiction Enforcement Act ("UCCJEA") the father can commence an action for custody/visitation here in New York, and you would have to return to allow the New York court to determine: (a) who should have custody; and (b) whether you should be permitted to relocate out of state with the child. (Each of these are complicated issues so I won't attempt to deal with them here; I have divorce guides on my website that might be helpful.) Also, some judges are offended when a parent moves out of state without the Court's permision.
The better course of action would be to reach a written agreement with the father in which he acknowledges and agrees that you are moving out of state. That way he can't later claim you moved without him knowing about it or that you absconded with your child.
Lacking that, you might want to start custody and child support proceedings in the NYS Family Courts (assuming they will accept new petitions, hopefully soon), get an order of cusoty, get a proper amount of child support, and get the court's permission to relocate.
Good luck.
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