By staying with him, you will be teaching your little girl that his behavior is acceptable. That will set her up for being an abused wife herself some day.
Be careful you are not using 'the only father she has ever known' rationale to conceal the fact that you are afraid to be on your own with your child.
He is a bully, which means if you leave him he will harass you, using seeing the child as an excuse.
But he will avoid paying child support, also, as a way to control you. So don't believe he loves the child deeply. Men who love their children want them to be secure and well cared for. They would never see their child go without the necessities just to harass the mother.
So you will be continually going to court to get his support payments, and he will delight in making you jump through hoops to get a few dollars a month.
But there is a way. It takes guts. See a lawyer and get him to draw up a separation agreement. You get full custody of the child, and can take her anywhere in the world. In return, you will not go after him for child support. Then be a mom, and you and your child start a new life.
Let's face it. If you stay with him, the abuse will continue, and only get worse.
It may well include the child later on, when she begins to show any spirit of independence. Then he will need to control her too, so the verbal abuse, and even beating, will start. Bullies delight in having someone small and weak to demonstrate their dominance on. They never stop voluntarily. And if he finds another woman, he will find someone weak and submissive who will put up with it. Possibly a child will be involved, to enslave her even more.
Such men cannot love. Don't kid yourself.
And when you meet a good-natured man who doesn't have a substance abuse problem, but does have a loving heart, don't worry about what he looks like or how much money he makes, as long as he works enough to get by. He's the guy for you.
How can you leave? Pack a bag of clothes for you and your child and walk out the door. Live in a shelter if you have to, until you get a job and arrange daycare. If you have friends or family that can put you both up until you are on your feet, so much the better. Though he will make trouble for them, count on it.
Become independent. I did. And my three children thank me for it to this day. We were poor. But there are worse things than poverty.