Your question isn't really "fair" because it assumes that Miss Jane Pittman is a real, live person. Nope. Miss Jane Pittman is a fictional character despite the title of the work, The Autobiography of Miss Jane Pittman which, ironically, is a work of fiction and, as such, a novel. However, your question about the CHARACTER of Miss Jane Pittman can certainly be answered.
The character of Miss Jane Pittman is a true pioneer in the civil rights movement. Why? Not only does she witness the end of slavery, but due to her extreme age when she dies, also get to witness emancipation and reconstruction and the Civil Right's Movement. Therefore, Miss Jane Pittman is not only a pioneer, but a pioneer who has persevered.
Now to the specifics of your question. As mentioned above, Miss Jane Pittman's character dies in 1962. [Please note that it is not really fair to use the film as the exact date (which is 7/19/62) unless you are referring specifically to the film adaptation in your question. This shows that Miss Jane Pittman's death truly was right in the middle of the quest for civil rights. Because the book does indicate that the character of Miss Jane Pittman was, in fact, 110 years old when she dies, this shows that due to her death date of 1962, she would have to have been born in 1852: almost ten years before the Civil War and deep in the heart of slavery in America.
Ain't we all been hurt by slavery?
In conclusion, it is important to say, however, that Gaines who wrote The Autobiography of Miss Jane Pittman certainly did get inspiration from real-life people.