Considering divorce with a 3 month old baby in the picture

Me and my husband are very different people and since we got a baby he became even more mean to me. I stay with the baby 24/7 while he goes to work. He expects me to do all house related tasks on top and doesn't help with much. Whenever I ask him to do something he ignores me or argues with me. The baby is very demanding and difficult (cries a lot)so i am constantly sleep deprived and struggling. Anyway, husband doesnt care about me and I am thinking to divorce him and get most custody for the child. I am however worried for the mental wellbeing of the baby and wouldnt want this to cause him trauma for life. Not sure where to go from here or how to handle things. I guess I could also stay in the marriage for the sake of the baby and just ignore my partner and not ask him to help me with anything...