Ooh this is a toughy!
Just remember that no matter if you divorce him you will forever have him in your life since you do share a child.
My heart goes out to you and in my opinion I don't see how he would be able to provide for a child if he isn't willing to work. But it will be in the judges hands to make that ruling, I would suggest that you keep up your good work on your side and take the plunge if you truly do not see that there is a way to work it out. If he is like my husband, he won't go to a marriage counselor and feels that he is doing nothing wrong. He is providing free day care, and that is an expense that you will incur once you move out if you do get custody, something to think about. Marriage is a two way street and I feel as if I give 90% in mine most of the time. But, I rely on the Lord to get me through the times that I feel as if I can't live with him any longer. Overall it is my faith in God and my attitude that has held my marriage together. My husband contributes 1/4-1/3 my net income to our budget and does nothing around the house to help out.
Good Luck and Best wishes on whatever you decide. May God Bless You now and always. My mom always says if the good times outweigh the bad then stick to it, if not - get OUT. Life is too short to be that unhappy. Make sure you aren't pms-ing, that is my worst time to feel as if I need a divorce.
M. (mother of 4 - boy/girl Twins 26 from first marriage, and son 18, daughter 16 from current marriage of 22+ years to a selfish husband that loves me in his on way.)