How does child support work? Ex doesn’t want to help

I’m currently unemployed with a 1.5 month old baby. I quit my job during my pregnancy and have been living off my savings. Can I still file for child support? I’m scared the judge will ask me why I am not working. I don’t plan on getting a job again until my baby is 6 months old but I’m scared it will backfire on me in court. Will my employment status affect me if I file for cs?

The father refuses to help me out financially. I have tried to be civil and express that it bothers me he does not help but he still doesn’t do it. The only gift he has given my baby is ONE ONESIE that didn’t even fit her. He just expects me to let him see my child when he randomly appears at the door. He refuses to arrange a set visitation schedule with me and doesn’t show up when he says he will.

I would like to clear out that he isn’t on the birth certificate.