I have the following info on Moody:

1850 census; Madison Co. TN, both Moody age 22 & brother Robert age 26, in the household of a Midyett family. Robert moved to TX before the war.

1860 Gibson Co. with own family

1870 Dyer

1880 & 1890 Crockett

died 1898, buried Crockett Co. TN.

Enlisted May 23 1861, served until Dec. 1864 (1890 census)

http://tngenweb.org/records/madison/records/colsteph.htm

According to family oral history he had a brother Allen, there is an Allen H. Young in Moody's company ( above link) so i believe this was most likely his brother.

Have never found his parents in any census records, as you know before 1850 names of children were not listed.

Thanks