I don't think this is Nicholas' father. NIchlas' brother George died in SC, while George son of this George Peay died in Wiliamson Co. TN in 1849. NIcholas is probably the son of George Peay of Caroline Co. VA. George & Nicholas Peay of SC had a brother Austin (1769-1839) who is also missing from the Rockingham records. The problem is there are several George Peays, probably all related:
1) George Peay & wife Elizabeth of Caroline Co. VA (1755)
2) George Peay & wife Mary of Caroline Co. VA (1757 - may be same as #1 with new wife).
3) George Peay b. Caroline Co. VA (1757) d. TN. (son of George #4 of Rockingham Co. NC).
4) George Peay (b.c.1740 d. 1804 Rockingham NC).
5) George Peay b. 1767, son of Austin Peay & Mildred Turner.
6)George Peay & wife Ann of King William Co. VA (1793).
7)George Peay & wife Elizabeth (d. 1791 Fairfield Co. SC; brother of Nicholas).

A Nicolas Peay, son of Elias Peay, was named in the will of Thomas Dalby of king William Co. VA in 1702. This is probably the grandfather of Nicholas, George & Austin Peay of Fairfield Co. SC.

4) George