Two girls named Dawson --Ann Dawson and Mary Dawson-- attended the Mordecai school in the same five sessions (latter half of 1816 to the end of 1818), both from Georgia. Safe to assume they were kin, and probably sisters. "Richard Blunt for the Misses Dawson" is an item in the school ledger for December 1816, and Richard Blunt is also mentioned paying for "Miss A Dawson" and "Miss M Dawson" in the ledger for February 1818; so they may be related to the local Blunts. Other than those mentions, there's nothing in the Mordecai letters about these two girls.
Probably the place to start is Richard Blunt, because we've already encountered a Richard Blount who was sending students to the Mordecai school. And that Richard Augustus Blount (1774-1849) lived in Georgia. And... his wife was born Mary Dawson. Her brother, John Edmonds Dawson, died in 1811, leaving five young children, including Ann B. Dawson and Mary F. Dawson, with Richard A. Blount as their guardian. (Here's their brother, Rev. Dr. John E. Dawson (1805-60), "a prince among men." This is a biography that their younger sister Annabella wrote about John. Annabella also wrote an extremely successful cookbook that's been in print for many decades.) Their mother was born Annabelle Burwell, which also links the Dawson girls to the Burwell families who also sent children to the Mordecai school (Lucy Burwell, for example, was at the school during the Dawson girls' time). Annabelle Burwell Dawson may have married a second husband after 1811.
So here's what we can find, from that connection:
Ann Burwell Dawson (c1804-1841) married Fortunatus Sidney Cook in December 1820, and had six children (Algernon, Anna, Mary Frances, Monimia, Barclay, and John). Ann was widowed in 1837, and died at Wetumpka, Alabama in 1841, age 37, at the home of her brother-in-law Henry Cook (see below). Here's her obituary. Her eldest son Algernon Marcus Cook became blind, possible in consequence of his service in the Mexican War. Daughter Monimia married the Isaac Taylor Tichenor, who later (years after she died) became the president of the Agricultural and Mechanical College of Alabama (now called Auburn University).
UPDATE 11/15: More about Ann's daughter Mary Frances Cook Noble (d. 1913) in the comments, from a descendant. Thank you, Lisa Slack!
Mary Frances Dawson (c1807-), Ann's younger sister, married Col. Henry H. Cook in December 1821, and had two daughters (Cordelia and Mary). She died in Troup County, Georgia, but I can't find a death date.
So.... from being the barest of sketches on the rolls in my dissertation appendix, Ann and Mary Dawson have become connected into the broad network of cousins who attended the school, and have their lives drawn in a bit more. Calling this entry a success! But if you know more about the Dawson girls, I'd love to hear about it.