I agree with GiveLove. It's important to just take a few minutes off today from even thinking about the "what nows?" and just breathe. This is a new gift you are allowed to give yourself now, with him out of the house. You will be busy enough with the kids and the baby. So start today with being what you might call a tad selfish, and give yourself 5 minutes or 50 minutes off, just to breathe, relax, and be mindless. It's very important to take a mental break from the awfulizing that goes on in the mind of a codie out-of-control with worry.
Do you have other family members who will help you in the immediate days here? How do you feel about not being married to this man? If it is a real choice you've been considering and were not sure how to make it happen, today could be your HP's way of giving you a BIG gift. I would ask you to think about that one seriously for a minute. If you do truly think that you want out of this marriage, then his leaving will actually be a big godsend to you. I know, I know, it sounds very calculating to think these types of thoughts right now, but in hindsight you might be glad you turned off the emotion for a minute and thought in a practical fashion.
He may think he's doing this to just scare you into letting him come home and continue to drink. What you get to do here, though, is realize that YOU don't have to EVER let that type of behavior come back in your door again if you don't want it. Personally, I would stand totally firm and not allow him back. He made the choice, I'd pack his stuff and say here ya go. He is going to sober up eventually and realize that he left his wife and child and probably regret the leaving. Don't be surprised if he calls withing the next day or two and is sorry and remorseful and wants to return. YOU DON'T HAVE TO LET HIM IF YOU DON'T WANT TO, because he left. That is the way a court will see it also. He left you and the child, not you leaving him.
THEN, if he would decide that HIS drinking is out of control and HE needs to do something about it, it will up to HIM to quit. YOU can breathe freely meanwhile, in YOUR alcoholic-free home with YOUR children who deserve a home filled with safety and love. You can also decide at some time in the future (IF he seeks treatment and sobriety) to try again at your marriage. BUT for now, YOU DON'T HAVE TO GO BACK to living that way any more if you don't want to.
Don't look at this as a rejection of YOU. Look at this as an opportunity for YOU to make a very necessary change in YOUR life and the lives of your CHILDREN. You all deserve a home that is free of violence and yelling and anger. That is NOT love nor is it marriage as it should be. Today you get to decide what YOU want. Not him.