First, you have inquired if active duty military personnel are exempt from the permit requirements. The exemptions are set forth in O.C.G.A. § 16-11-130. I note that this Code Section exempts certain persons from "Code Sections 16-11-126 through 16-11-128." Thus, persons so exempt are exempted not only from the requirement of a permit to carry a firearm (O.C.G.A. § 16-11-128), but are also exempt from the provisions regarding the carrying of concealed weapons (O.C.G.A. § 16-11-126), carrying deadly weapons to or at public gatherings (O.C.G.A. § 16-11-127), and carrying weapons within school safety zones or at school functions (O.C.G.A. § 16-11-127.1) But see O.C.G.A. § 16-11-127.1(c)(3), which appears to limit the exemption to persons actually participating in military training programs.
Under prior versions of this statute, it was clear that the exemption applied only to the performance of official duties. See, e.g., Talley v. State, 129 Ga. App. 479, 481 (1973); 1987 Op. Att'y Gen. U87-28. However, at that time the exemptions applied to these persons while engaged in the pursuit of official duties or when authorized by law. Since that time, the statute has been amended. Official Code of Georgia Annotated § 16-11-130(a) now provides that the exemptions apply to "persons . . . employed in the offices listed below." Persons in the military service of the State of Georgia or of the United States are among those so listed. O.C.G.A. § 16-11-130(a)(3). Thus, it is my unofficial opinion that active duty military personnel are exempt under Georgia law from the requirement for a firearms permit.
Secondly, you have asked if the exemption is limited to the performance of military duties on the base. As noted above, under the current version of the statute, persons so employed are exempt; the statute no longer limits the scope of the exemption to the performance of official duties.
Thus, my response to your question is in the negative.
In your third question, you ask if active duty military personnel may, notwithstanding the exemption, apply for and be issued a firearms permit. Permits may be issued only to a resident of this state whose domicile is in the county of application. O.C.G.A. § 16-11-129(a). Generally, military personnel are not residents of Georgia and thus they were not eligible for the permits under a former version of the statute. See 1976 Op. Att'y Gen. U76-71. Under the current statute, however, an active duty member of the armed services who, although not a domiciliary of this state, resides in the county or on a military reservation in the county may nevertheless obtain a firearms permit if otherwise eligible. O.C.G.A. § 16-11-129(a). Thus, it is my unofficial opinion that a member of the armed services may, provided that he is otherwise eligible for the permit, apply for and be issued a firearms permit notwithstanding the fact that he is not domiciled in Georgia.