A couple of things....if you are looking for the parents of a woman born 1822, why not look at the 1820 and 1830 census records. She should be age 8 in 1830 census, look in 1830 at Donelson / Donaldson and see if any have a female age 7 or 8. Have you done that?
Now for the Andrew John Donelson born 1767, in 1780 when Nashborough was settled he would have been about age 13 so you are looking for his father? Col. John Donelson Sr is D.A.R. info on him - Apparently he had sons John Jr., Leven or Severn, Samuel, Stokley/Stockley, William. Could Andrew John have gone by John?
entry for John Donelson Jr.....son of Col. John Donelson, Sr., came to the Cumberland settlements on the Donelson flotilla, 24 april, 1780, with his bride, Mary Purcell, had 3 taxables in 1787 Davidson County. I don't think this is your Andrew John as he would have been only about 13 in 1780 and that is a bit young to have a bride.
The James Donaldson who came to Cumberland Settlements from Natchez in 1783, an inventory of his estate delivered to court July 1796. You might check that.....I don't know of his relationship to John Donelson if there was any.
I looked in Pre-emptors - land records and found on Stevens:
242. Lawrence Stevens obtained a pre emption of 640 acres of land lying on the No. side of Harpath river 15 miles of the French Lick about two miles East of the Lower So. road to include three Aprings marked at the head thus L S on a poplar, to begin on a ridge South of the Springs and to run down on both sides of the branch at the Law directs.
243. Joush Stevens obtained a pre empn of 640 acres of land lying on the West side of Stones river on the first big Creek above Stewarts' Creek a mile above the mouth of sd Creek, begin'g 1/4 of a mile West of the spring on the Creek, and running down on both sides of the Creek including a tree marked thus J S.
Payroll of Militia Officers and Soldiers on an expedition against the Chicamauga Indians in 1787 from Davidson and Sumner Co TN....
Voucher # Name of soldier County Date served
458 Donalson, Jacob Davidson 13 Jan 1790
288 Donalson, John Davidson 13 Jan 1790
468 Donalson, John Davidson 13 Jan 1790
413 Donalson, James Davidson 13 Jan 1790
382 Donelson, John Davidson 13 Jan 1790
386 Donelson, Robert Davidson 13 Jan 1790
429 Donaldson, Wm. Davidson 13 Jan 1790
--- Donelson, Wm. Davidson 13 Jan 1790
Under Donelson I will give you part...
123. John Donelson ...640 acres..in the fork between Stones river and Cumberland.
318. Joel Hobbs...640 acres..on a branch of Harpath river adjoining John Donelson's pre empn who was assee of Peter Vardeman.
150. John Donelson Senr. assee of Peter vardiman...640 acres..branch of big Harpath river & on the East side of the River about 3 or 4 miles West from Isaac Drake's pre emption & about 4 miles from the River 3/4 of a mile from a Spring....
232. John Donelson Junior obtained a pre emption of 640 acres...on the West side of big Harpath river about 1 1/2 miles above William Pannel's pre empn abt. 1/4 of a mile above a small creek .....
258. William Donelson ...640 acres...on the Sulphur fork about 7 or 8 miles below the Sulphur Spring which is a branch of red river.
the above pre-emptors the info was taken late 1782 and 1783.....people living on the land at that time.
I think you have to look at 1830 census and then go back from there. Jumping all the way back to 1780 is skipping a lot of time.