Any time you alter a building in the state
of Tennessee, even accessory structures or non enclosed structures you will need a permit. The only time you wouldn't would be if it was aesthetic finishing changes, painting, wallpaper(for interior) or staining etc..
You would need one for any alternation, erection or demolition, movement and even unfortunately even for repairs. Also, your permit will require inspection during the process.
So yes, even if it was an "old repair"*(and I use the " " heavily) to enclose a once "there" door, and you are caught without permit, you will end up paying fines probably costing more than a few permits themselves as well as the trip themselves. If it goes past the realm of basic repair, you need a permit.
Since you are outside the city limits, the need for a permit still applies
Here is your web listing for Gibson(city of) http://www.gibsoncountygov.com/local-government/gibson/
And Gibson County, which I believe is the one you have to use since you are out of the city limits http://www.gibsoncountygov.com/local-government/county-government-contact-information/
Just for reference, to be safe, even though its a separate structure(your unattached porch) if the county would have deemed that a non-repair(your word vs theirs) you would have gotten in trouble as you needed a permit, so you definitely should get one this time for your carport.
Good luck during your build Jeff