Unemployment is for part time employees as well. Just go to their website and file online. It shouldn't take to long to hear back. It's worth a shot.
You could just keep working until you get closer to delivery to make the extra money, unless your doctor is putting you on restrictions so you can't work at all... you can't get unemployment for voluntarily leaving your job especially if you're going out on FMLA - in that case you're still employed just not working. You can only get unemployment if you're laid off due to lack of available work or fired for unjust cause.
You can apply for welfare and food stamps.
You cant be on maternity leave and collect unemployment you can file for short term disability but thats all and it also depends on your job most benefits arent available to oart time employees talk to your human resource manager about it she/he would know the best answer