Thanks, Father, but Georgia is a weak spot: I don't speak the language.
If you want some academic stuff:
Ancient Christianity In The Caucasus, Volume 1http://books.google.com/books?id=PkZjdVAzsvIC&pg=PA7#v=onepage&q&f=false
Studies in Medieval Georgian Historiography: Early Texts and Eurasian Contextshttp://books.google.com/books?id=nCFwaxMumWkC&pg=PA91&dq=Ancient+Christianity+in+the+Caucasus&hl=en&sa=X&ei=bbwlUYyDCqTA2AWWlYEQ&ved=0CEEQ6AEwAw#v=onepage&q=Ancient%20Christianity%20in%20the%20Caucasus&f=false
Iberia between Chosroid and Bagratid Rule by Cyril Toumanoff (a leader in this area):http://rbedrosian.com/Ref/Toumicb/toumicb.html
A primary source translated:
Rewriting Caucasian History: The Medieval Armenian Adaptation of the Georgian Chronicles - The Original Georgian Texts and the Armenian Adaptationhttp://books.google.com/books/about/Rewriting_Caucasian_History.html?id=MVBEwzIoAOAChttp://www.erevangala500.com/uploads/pdf/1323119167.pdf
The Georgian Chroniclehttp://rbedrosian.com/gc1.htm
Some Encyclopedia articles:http://books.google.com/books?id=PkZjdVAzsvIC&pg=PA7#v=onepage&q&f=falsehttp://books.google.com/books?id=fWp9JA3aBvcC&pg=PA137#v=onepage&q&f=false
A bit dated:
A short History of the Georgian Church: Translated from the Russian http://books.google.com/books?id=9bIAAAAAcAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
Seeing Islam as Others Saw it: A Survey and Evaluation of Christian, Jewish, and Zoroastrian Writings on Early Islam, by Hoyland has a survey done by someone (I don't know offhand where I've left my copy) on the writings in Georgian on the Early History of Islam, the Islamic invasions etc.
There are also a lot of bits and pieces here, there and everywhere on Georgia: it comes up in the histories of its neighbors a lot.