First off, good for you for not listening to your ex. He is the fool, not you.
At this point you need to calm down (hard I know, but you need to) and just give the future a thought. Our Lord has entrusted you with the life of a baby, always remember that. From His hands that child has come to you, but all that means is that you have to do everything you can to look after yourself, and do the best for the child.
Now, take a few days to think about things yourself. Maybe ask your priest, your friends and your family for advice. If your parents are less than enthusiastic about the whole thing, just know that they are only scared for your future and that might cloud their judgement. Whether you decide to raise the child, or give it up for adoption, know that your parents will see sense eventually, sooner or later, just don’t allow anyone to push you into making the worst decision of your life. I’m so happy you see that you know abortion is not an option, or a solution. Whatever happens next, your life will be changed forever. The thing is that you have chosen the happy route, the one where a whole new person gets to come into the world! So many women are forced to make the “choice” and as one said to me once " I always look at my kids at the dinner table and no matter what I know one more should be there too", gladly you will be spared that because you are a smart, brave woman!
To answer your question, YES, absolutely single mother families work. I know so many single mothers and their kids are fine. Some of the fathers are in the picture, some aren’t. Whatever the case, a loving mother is all a child needs. Nor does it mean that you will be condemned to a life of poverty. The vast majority of single Moms I know are very successful, so remember that.
If you decide you don’t want the father in the child’s life, I wouldn’t worry too much about going into detail with your parents about why. Just tell them that he isn’t being supportive and that since you are broken up his role would be extremely limited anyway.
I’d talk it over with trusted people, go and see a lawyer and pray for help and guidance. I’m praying for you.