Not sure where to start, HELP

So my boyfriend and myself have been friends for 8 years and in a relationship for 2 years. We just had our first child 4 weeks ago and things are getting worse. He has a drinking problem that I didnt know about until almost a year into us being together. (Didnt know because I dont drink and we weren't living together until this year). I've held him accountable with getting help, because i just wasnt going to leave then. I've helped him reach out to therapists and local support groups. I even suggested we go to counseling together to work on our relationship, because we dont communicate well with one another and he's agreed to all of it, but never acted on it.

I don't think I want to be with him anymore. I love him, but at this point I'm thinking about my daughter. I don't want her to grow up with a drunk father in the home. We have our home and baby girl and I have no job. He's paying everything and i am very grateful and I make that known all the time. When I do get money from school or my parents, I try to help out as much I can. I even cook and clean. I got a new amazing job some time before I had baby girl. I tried submit for maternity leave and they said I hadn't been there long enough. My only options were to quit or come back to work the next day. That's freaking insane. So that has us both over the edge, because I dont have a job right now.

I just feel overwhelmed, a bit frustrated, depressed and tired as hell and I feel sometimes he's a bit inconsiderate towards that, because he doesn't understand. All we do is argue now and then makeup, but it never gets any better. I want to leave, but I have no idea where to begin. Any advice would be extremely appreciated.