First what state are in?
Second, the chances of him getting full custody are slim to none. He can make idle threats, they are great at that. But they usually lead no where. Unless he has good reason and can prove you unfit he is highly unlikely to get full custody. In fact, he is likely to get little custody of your daughter after birth on a count of she will be so little. There are some very liberal (meaning they like for both parents to have as equal time with the kids as possible) states out there, one of which I live in, California. We went through custody of my infant son (he was 5 months old) and my 1 1/2 yr old daughter and the father got very little custody. There was nothing to prove either of us unfit. The schedule increased every three months to a little more until my son was done breastfeeding and we are now on an every other weekend and and a dinner (3 hour period) once a week. They are 2 and 3 1/2 yrs old now. My ex also went for sole custody, tried to "prove" me unfit but couldn't. This is our permanent schedule.
So try not to worry and don't let him threaten you. I would suggest a very good lawyer though. Custody battles are very messy and are compiled with complicated procedures and paperwork. It is not a do it yourself kind of thing!
P.S. unless he is on the birth certificate, signs an Affidavit of Paternity or gets a DNA he has no legal rights to your child and is not considered the legal father until a court order is issued.
Check out both of these posts for further info:
http://www.askmehelpdesk.com/childre...tml#post418122 http://www.askmehelpdesk.com/childre...tml#post409325
Good luck!