There's a student on the roster of the Mordecai school that I compiled in the early 1990s named Sarah Fauquier. She's listed as being from Norfolk VA, attending for both 1818 sessions, and having William Fauquier as the adult on her account.
There is a Fauquier County in Virginia--but the name is probably still variously spelled in early 19c. sources, including Farquhar, Forker, Falkier, etc. And Sarah might also be Sara or Sally. But we have a parent(?) name and a city, which is a good start. And attending only in 1818 means she's likely born a few years after 1800--looking in the vicinity of 1805 would be best.
A Sarah Fauquier, daughter of William M. Fauquier, married at Benjamin Emmerson at Norfolk on November 10, 1824--that Sarah seems like a very good candidate, age is a good match, everything else lines up.
A William May Fauquier (1773-1827) was a chemist in Norfolk VA, and appears as "William M. Forguher" in his wife's family bible; he married Ann (Nancy) Benthall in 1801. They seem to be the parents of the same Sarah (Sally) Fauquier Emmerson above; that woman, born 1804, named one of her eight children Anna Benthall Emmerson. William May Fauquier was a deacon at the Baptist Church in Norfolk.
Is she the one? Anyone with further useful information, please share in comments.