OP I've been in your position, ExP was very much the same, though we didn't have a child together. It was the prospect of having a child with him, and the position I would be putting myself in, that was part of the reason I left him.
We had been together 13 years, it was for me, like you, the first real relationship I had had. Many years of the relationship were, I have to admit, spent going out, partying, having a good time. It was only after I grew up a bit, took a much more "take it or leave it" attitude (actually I just left it!), that I realised he was unable to leave it and his whole existence centered round his need to have enough drink to hand, and to consume it in large quantity every day. He had a good job, went to work every day, and said it was his way of "relaxing", switching off after work. The fact was he would start drinking the minute he got in, until he passed out on the sofa, or staggered to bed. At the weekend, midday was the starting point, but sometimes from breakfast, sometimes he was still going from the night before. He was in complete denial that he had a problem. There was not a single day where he didn't drink to excess.
He was emotionally abusive, I later came to realise, very controlling. His behavior in public was often embarrassing, he was aggressive about other people but under his breath to me, possessive, jealous, difficult. Because I had been with him "forever" I couldn't imagine not being with him, for a good while I didn't even realise that I didn't want to be with him. I was in denial... Eventually things came to a head, and we broke up. I realised the next day that this happened while he was extremely drunk (you know sometimes it was hard to spot how drunk, so accomplished a drinker he was), and he used his being drunk as an excuse for saying he wanted us to give it another go as he hadn't been able to put into words how he felt. It felt for me like Groundhog Day!
Eventually I did leave, and god was it the right thing to do, I am infinitely happier now in a balanced, fair, supportive, loving and passionate relationship, with an emotionally independent person. We have one DD, and her arrival has been joyous.
This is long, I'm sorry - but I know all too well how you feel, my experience and the change I made is something close to my heart, it was life-changing. It's easy for people to say "just leave", but after such a long time together, with a baby, it may seem impossible - it may not even seem like what you want. Only you can decide what you what for your life, for your baby's future, and make it happen when your strong enough. Unfortunately, in my experience, people don't change.
A friend once said to me, while I was still with ExP, "does it feel like you're at a football game, and everyone's playing, but you're watching from the edges?". That summed it up perfectly - now I'm actually playing.