She and my son(just tuned 1) live in my house where I support them both, I am on the birth certificate, now she is threatening to move away and take my son with her, can she do that? He has lived in MY home since birth,

And we live in Texas

Yes. She can unless you get a court order otherwise.

You should go to an attorney about this immediately.

The mother could just move without doing anything through the courts, which would force you to fight through the courts to get the child returned. It's much easier to stop it from happening to start with by asserting your custodial rights over the child.

Your attorney can do a couple of things. First, they can petition the court for shared or primary physical custody of the child. Second, they can ask the court to issue an injunction to stop the mother from removing the child from the state pending the outcome of the custody order. Third, they can advise the court that you object to the child being removed from the state, forcing the mother to pursue a removal action in court if she wants to remove the child from the state.

It is difficult for a parent to win a removal action because the bias of the court is that the child benefits from regular contact with both parents. To deny the child that frequent, close contact with the non-custodial parent can only be done if the custodial parent can demonstrate that it's in the child's best interest to move.

Your girlfriend hasn't even established primary or sole custody, so right now you have equal rights to this child. If she moves, and enough time passes, she can establish residency of the child in the other state, making it increasingly difficult for you to get the child back with you.

So, waste no time - hire an attorney. She does not have an upper hand here, but will if you do nothing.

Thank you all for the quick response, I'm on it!