Cases are not dismissed merely because you have a different story than the other side. Otherwise, there would never be any trials or lawsuits because everyone's answer would say the plaintiff is wrong. A judge has no reason to believe you over the nanny at this point. Unless you settle, there will be a trial and the judge will review whatever evidence there is, and choose to believe one side or the other. Since you are the party who has more to lose (not the money - but a judgment that will follow you around and harm your credit for years), you need a lawyer now and needed one before filing your answer.
I think you are telling us that you are being sued in small claims court, and that your nanny says one set of things about the facts, and you say another set of things about the facts. Generally speaking, when the material facts are in dispute, a hearing is necessary, because courts aren't supposed to make determinations on genuine factual disputes without a hearing.
Sometimes where facts aren't in dispute, a court can dismiss a case either because the plaintiff's complaint doesn't state a claim (i.e., even if everything the plaintiff says is true, the court can't grant relief), or because the material facts aren't in dispute and the party that asks for the dismissal proves entitlement to judgment as a matter of law. But I suspect on the facts you describe above that the court will have to have a hearing to sort out what the real facts are.
Not legal advice as I don't practice law in Georgia. It's just my two cents on the facts you describe based on some general principles of law. If you need legal advice, please consult Georgia counsel. I practice in Vermont ONLY.
I don't know how much money is at stake in this litigation, but I suggest you spend the money to consult with an attorney for thirty minutes to an hour and obtain some advice regarding your options. Good luck.
Sounds like a he said nanny said issue. You are going to need a lawyer. if it is magistrate court, however, to pay the debt may be easier and cheaper than hiring a lawyer.