Its always good to get a custody agreement put on paper regardless of if you and the child's father get along well. As far as I know in TX you get to keep ur kid unless someone raises questions about your ability as a parent.
I'm in Texas too, and I'm not married to my unborn baby's father. I'm still trying to figure it out, but the way I understand it is that until the paternity document is signed and paternity is established, he has no legal rights over her. Since we are trying to do this together, he'll do that and then (from my sort of vague knowledge of it) we both have equal rights over her, or depending on what a court orders he definitely has rights to visitation and such and has to pay child support.
We've discussed it and both he and I agree her primary residence will be with me, but he'll have the right to take her at least a couple of times a week, some weekends, etc., depending on his work schedule. As soon as she's born we're going to map out a basic plan for both weekly custody and holidays, etc. I'm insisting we go to a lawyer to get a legal custody agreement to make it official.
We're trying to do a lot of it informally and I'm okay with him dropping by to see her whenever we're free, he's trying to be a good dad and I think it's best to encourage that...but as I told him, I'm not willing to risk her happiness if either of us goes insane for some reason and we start acting immature. We're friends so hopefully we won't need it, but it doesn't hurt to have the legal document as a failsafe. The court can do that for you as well if you're not really on good terms with him. You should check out the Attorney General's office and maybe give them a call, they could probably tell you more than I could. If you find out anything new, definitely let me know.
https://www.oag.state.tx.us/ag_publications/txts/paternity.shtml