Ah, I thinks me just answered me own question:
(a) Application for license; term. The judge of the probate court of each county may, on application under oath and on payment of a fee of $15.00, issue a license valid for a period of five years to any person whose domicile is in that county or who is on active duty with the United States armed forces and who is not a domiciliary of this state but who either resides in that county or on a military reservation located in whole or in part in that county at the time of such application, which license shall authorize that person to carry any pistol or revolver in any county of this state notwithstanding any change in that person´s county of residence or state of domicile. Applicants shall submit the application for a license to the judge of the probate court on forms prescribed and furnished free of charge to persons wishing to apply for the license. Forms shall be designed to elicit information from the applicant pertinent to his or her eligibility under this Code section but shall not require data which is nonpertinent or irrelevant such as serial numbers or other identification capable of being used as a de facto registration of firearms owned by the applicant. The Department of Public Safety shall furnish application forms and license forms required by this Code section. The forms shall be furnished to each judge of each probate court within the state at no cost.
Sounds like, according to 16-11-129a, that the permit is valid despite a change in county residence. Did I read that correctly?
I am probably going to need mine where I am going.