LDS and RootsWeb sources give his name as Andrew Jackson with the parents you had mentioned. LDS sites also lists your Jackson L. Garrett as dying in 1860.

Do you know if the 11th Georgia and the 8th Georgia were cever consolidated? I have found this ---

http://home.earthlink.net/~larsrbl/CoB8thGARoster.htm

Garrett, J. L. ------ private May 21, 1861. Wounded and captured at Gettysburg, Pa. July 4, 1863. Died of smallpox in Marine U. S. A. General Hospital at Baltimore, Md. January 8, 1864.

http://www.itd.nps.gov/cwss/soldiers.cfm
Jackson L. Garrett (First_Last)
Regiment Name 8 Georgia Infantry.
Side Confederate
Company B
Soldier's Rank_In Private
Soldier's Rank_Out Private
Alternate Name J. L./Garrett

Except for the CWS&S I have not been able to find J. L. Garrett in the 11th Ga. Inf.

Do you know about when his last child was born and what county in Georgia?

GP