Alabama handgun laws, for your perusal and edification
teknoid;
Luke has thoughtfully provided the information you seek.
From the top of the page, select "Permit Maps".
From the map page, left-hand column, sixth line down, select "Laws and Permit Info".
From that page's main column, select "Alabama".
This will bring up all the relevant legal aspects of Alabama carry.
The gist of it is, in some places and under some conditions (according to an AG opinion which I can't find here but of which I have a copy) open carry while on foot is allowed. Wouldn't test it, however, as most LE may not be aware. I'm sure you don't want to "beat the rap, but not the ride".
At any rate, when you leave your feet and enter your car, you'll need your permit and must carry "concealed". Glove box or console is probably OK.
Happy reading and everyone please remember that the title of Luke's site is
"Concealed Firearm Information and Resources".
Respectfully,
ElZorro