I have done the buy a trailer in SC, transport to GA a few times. If you can title the trailer in AL do so. It makes it easier to sell later.There is a market out there in stolen trailers, especially in states like SC and AL where a title is optional, and having a title will help you prove it is not stolen.
Contact your insurance company or agent and tell them what you are doing. They can arrange for insurance right away. Don’t wait until you get the trailer back to AL. If the trailer is wrecked while you are driving it home, then you are screwed. Same with a traffic stop where proof of insurance may be asked for. Then there are the Department of Agriculture police. You could get pulled over in GA without a tag by any cop, but the Georgia DOA loves pulling over horse trailers, especially near the state lines. They primarily are looking for current Coggins and health certificates, but even empty it can happen. I know this from personal experience in GA. Bottom line, get your paperwork in order before you pick up the trailer so you have both insurance papers and a temporary paper tag to display.
It is up to the buyer what form of payment they will accept, Personally these days I would not take a cashiers check because of the many ways to counterfeit them.
Finally, make sure all the trailer lights are functioning with your truck after you hook up, just in case you end up driving after dusk for some reason. You don’t want to be without trailer brake lights and turn signals either, as the lack of them can precipitate a traffic stop.