In Ch. 9, how does Douglass come to know the date?
It is important to read Douglass' narrative carefully. He was a masterful writer who chose words very carefully. In the beginning of Chapter 9, Douglass writes "I have now reached a period of my life when I can give dates." This does not tell us that he has suddenly become aware of the date, but rather that he feels at liberty to disclose the dates.
Just previous to this chapter, when Douglass is sent to live with Master Thomas Auld in St. Michaels, he had been living in Baltimore. This city is the scene of his transformation, to which he credits learning to read and write. In Baltimore, Douglass made a practice of trading bread with the little white boys on the streets in exchange for lessons in reading and writing, giving literal bread for the bread of knowledge. Indeed, he writes that the only attachment he has to his hard life in Baltimore is to "those little Baltimore boys." Further, "I had received many good lessons from them, and was still receiving them, and the thought of leaving them was painful indeed."
What would have been the consequence of Douglass giving details, such as dates, about his time in Baltimore? Certainly his little white teachers/friends would have been endangered by this information. Douglass is too savvy, and too gentle of spirit, to put them at risk. Once he leaves the city, however, he feels at liberty to fill in the details of his life.