I work for a small company, which does not have to abide by FMLA - although my employer said I can take 12 weeks off and come back to my regular position. They will only pay for 2 weeks off of this time though.
We do not have a short term disability plan either.

My insurance company recommended calling the state unemployment office to see if they will cover any type of disability pay since my employer is not covering this time off. I have talked to several people at the unemployment office and they don't have a clue as to what I'm talking about.

Are there any options I have to receive some sort of pay if I take time off after the baby is born? 2 weeks is not nearly enough pay, I would really like to take off 12 weeks and I just can't do it with limited income for those weeks.

Just so you know, even if your employer were subject to FMLA, that is unpaid time. California is the only state which mandates paid FMLA, and while I could be wrong about this, I believe CA only requires paid FMLA in some circumstances.

I will be very surprised if you are eligible to collect benefits from the unemployment office while you are on maternity leave. In the large majority of states, and I can find no information to suggest that Illinois is any different, you must be out of work through no fault of your own, be able to work and be actively seeking work in order to collect. If you have not been released to work by your doctor, you are not able to work or actively seeking work, and if you have been released to work by your doctor but want to take baby-bonding leave, you are no longer out of work through no fault of your own. Work is available to you; you just aren't working it. Thus at no time during your leave would you meet the requirements to collect benefits. If no one at the unemployment office knows what you are talking about, that's a very good indication that no benefits are available.

Employer-provided short term disability benefits are optional in your state, and only five states provide a state disability benefit - yours is not one of them. So no, I am not aware of any options for you to receive pay of any kind while you are on maternity leave. Sorry.