I commend your choice of having the baby rather than not. I also agree that letting an irresponsible alcoholic "father" have any rights would be insane. I'm not sure how the legal system is these days, if he actually has any rights or not. There are probably social services where you can talk to a lawyer & find out for sure.
In spite of some tough times, raising my sons was the most rewarding thing I've ever done. And I did it as a single parent for many years. The ongoing hell of dealing with an ex who is fighting over the kids is just awful, so don't get roped into some legal arrangement with the baby's father unless you really want to complicate your life for the next 21 years.

Only you can decide what you think is the right course of action, but know that many of us offer advice based on life experience...but

Please, rethink starting a new relationship at this time, you already have so many changes going on in your life. This baby should be the only new relationship that is a top priority right now. It is a relationship that will last the rest of your life, and it's going to take all your energy & time for a while. "Motherhood" totally redefines "full time". Plus the emotional changes you'll experience, (you can't imagine )... throw a new man in the mix and you may find yourself very mixed up. Your baby needs you 100% now.

Good luck!