How she came by that date: As you will see in the next paragraph, the answer is "the hard way."
What actually happened: Charles Mackay's 1841 book, "Extraordinary Popular Delusions and the Madness of Crowds," describes it thus:
"Great numbers visited the spot, and examined these wondrous eggs, convinced that the day of judgment was near at hand. Like sailors in a storm, expecting every instant to go to the bottom, the believers suddenly became religious, prayed violently, and flattered themselves that they repented them of their evil courses. But a plain tale soon put them down, and quenched their religion entirely. Some gentlemen, hearing of the matter, went one fine morning, and caught the poor hen in the act of laying one of her miraculous eggs. They soon ascertained beyond doubt that the egg had been inscribed with some corrosive ink, and cruelly forced up again into the bird’s body. At this explanation, those who had prayed, now laughed, and the world wagged as merrily as of yore."