I would begin with your extended family. You may have already tried this route---and I have no idea what circumstances are like. This can be difficult, I know, but the government is just a different kind of family. Perhaps an individual or a group of folks may be able to help you for a time? By providing cash or some kind of bartering assistance (reduced rent, pick up car insurance costs, yard work, housecleaning services, etc)? Next, I would investigate whatever religious/spiritual/civic organization you belong to. Often, such groups have funds set aside for assisting people in specific need. Third, I would look into a community foundation/grant maker. Even if they cannot support you directly, they will likely be aware of what resources are available in FL. There are also some great books available which can help you strategically plan the next year out, so that by your child's first birthday you could be a SAHM. Check out the local library. They can usually acquire books through interlibrary loan if they don't carry such a book.
You also asked about marriage? Yes, I would get married, but not if your the reason is to stay at home with this baby. Good marriages (usually, but not always) provide benefits to couples, to children, and to society as a whole. But bad marriages often hurt all three. If your financial situation changes over time, how would that affect your decision to marry? As for the legal effects of marriage, I have no idea how it impacts government subsidies and local law. I can only speak from my experience. Overall, it has increased our tax burden. But then, I didn't marry my spouse because he was a tax break.
I married him because he was my soul mate, he shared the same goals, and because I couldn't imagine myself not being *one* with him.
Good luck. There is a solution waiting just around the corner.