The most-likely candidates for her parents are John Thomas Fairchild (b. ~1750 in SC, d. ~1825 in GA; son of Capt. John Fairchild and Rachel Porcher, both b. ~1710) and Mary A. Brooks (b. ~1750 in SC). In 1790, they lived in Orangeburgh District (North Part) SC, on the Old Stage Road between Augusta and Ninety-Six. The census shows them with 5 females in the household, including wife Mary, daughter Mary b. ~1795, and (possibly) daughter Abigail Sarah b. ~1770. She was buried in Batesburg SC, but it is not clear whether this was before or after the 1790 census. He had at least 2, and possibly 3, unidentified daughters in the household at the time. He does not appear in the 1800 census for either SC or GA, but was living in Wilkinson Co GA at the time of the 1820 census.
His brother (or half-brother) William Fairchild (b ~1763 in SC, d Sep 1833 in Hinds Co MS) and wife Sarah Brooks were living in Edgefield Co SC in 1790. The two females in his household by then were wife Sarah and young daughter Elizabeth by a previous marriage (so no room for another Sarah). They were living in Jasper Co GA in 1820, left for MS with a group of in-laws shortly afterward.
Yet another brother Abraham (b 27 Jun 1762 in SC) headed west before 1803, had no children before 1790, later had family in MS and LA, but isn't documented in GA en route.
So probably you're looking for John Thomas Fairchild as a likely father for Sarah/Sally. At any rate, Capt. John Fairchild (Ranger Captain during the Indian Wars, J.P. and Deputy Surveyor for Orangeburgh and other back-country areas) would definitely be the grandfather of a GA/MS/LA Fairchild of that generation.