I don't think a DNA test can be done until the child is born. You could request one when the child is born, but I think the key here is knowing where she is when the child is born.
There really isn't any way you could keep her in the state, no matter what kind of paperwork you file.
If I were you, I would be as nice as I could to her, wishing her all the best and asking her to please stay in touch with you, just so you might know that she is OK.
And then, if she does it, and you know where she is, file for custody and most likely a DNA test will be ordered to prove
paternity.
It's a tough road, but not impossible. You might want to check out some of the info on this site to help you with your fight.
Best to you.