Online I am getting varied DOB of Hannah Parker who married William Earp. The latest I saw was 1820.
I also believe that the DOD is wrong on her and the son of William and Hannah, Henry Earp. You list him as living only one year and dying in 1844. There is a William Earp family listed in the 1860 Upshur County census: William, 58 years, Hannah, 50 years and Henry, 17 years. They live very close to Alexander Earp. At that age, his DOB would coincide with your DOB, but he seems to have not died in 1845.
If Hannah was 50 in 1860, then her DOB would have been ± 1810.
Do you know if this Hannah was born a Parker or might have been widowed before marrying William Earp? I am searching for a relative, Hannah Tipton, DOB between 1810 & 1820 who was born in Virginia (as the Hannah Earp in the Upshur Co. Census), and moved to Northern Alabama as a child with her family ca. 1820. She is listed in Tipton records as marrying an ARP (often used instead of EARP) and moving to Texas.