I am not sure if I can help. I am mother of one and he is 14 months now. I remained with my parents for first 3 mnths post delivery and then returned to my husband. I quit my job as there is no one else to take care of my kid. Trust me being non working is good but only for a month or so and then you start feeling worthless. So your good point is that you have a job.
It takes time for a father to sink in fatherhood, to understand responsibility and to share liability. He will never come to know what all are his responsibilities as a father and a partner in parenthood. This happens normally with every man. The best is that you try to make him realise. Discuss things with him. Divide your work and talk to him about this. Also divide baby sitting so that he knows when he is suppose to be with child. See he has seen you doing everything at your own for 9 months so now he feels you are capable of handling it. You have to share this with him that how difficult it is for you to manage and how much you need hus help. Talk to him to find out solutions best suited for two of you. Don’t get upset or disappointed. It is natural and happens with everyone. All you need is to talk your heart out with your husband. And planned or unplanned but now the child is responsibility of both parents not of any single one. Lack of sleep is matter of few more months. But don’t create this a habit of handling everything alone.. you have to make your man realise that what it takes to be a father and don’t worry he would understand you. Just be patient with him and with yourself. Good luck. Let me know if it worked