Maternity Leave

I live in the US, and I won't qualify for FMLA due to dealing with hyperemesis (it's caused me to miss work- enough where I won't meet the hours worked requirement- 1250- for FMLA). I don't live in a state that offers any extra protection or coverage. I know I'll need to talk to HR, but worst case scenario, would a doctor's note for at least a few weeks off after I give birth (I'd like at least two, though more would be nice) be acceptable? I'm not wanting to go early or anything like that. I've done some googling but couldn't find anybody in a similar situation and was wondering if any of you ladies have been there, done that and could offer advice. Thanks in advance :)