I don't doubt that she knew her own date of birth, but there are many reasons she might have lied about her age. If the first part of the interrogation is any indication, when they found her she was also lying about her name, or rather using her mother's name, Carraut. In any case, all the other information she gives fits with the other documents concerning her, which can only lead to the conclusion that she was either lying about her age or whoever was doing the writing either misheard her or didn't write clearly.