Doctors Note for leave

Hey guys quick question. So my employer will give me 6 week paid and if I want to take more I can however it will not be paid unless I have a doctors note. I really want to be with my baby for the first 3 months of her life at least. Totally feeling down about this. Do you think a doctor would understand my situation and give me a note or not really. I can’t afford to take extra time off without pay and I refuse to not take care of my baby till she’s at least 3 months. What should do?