Well, a gallon is kind of a gray area and is about the most a regular person is going to make, myself included.
For that kind of quantity, I'd recommend just keeping one of those 6 pack cooler things in the freezer. When it's done, serve the soup as usual, then drop the 6 pack thing in the pot and put the whole pot in the fridge.
This is, of course, assuming you're going to eat it in the next few days. Otherwise, you'd probably do better to split it up into servings via tupperware and throw into the freezer.
If you have a temperature probe, you can look at the results yourself. The impact of even one of those freezer packs is huge. It will drop the temp 30+ degrees extra in an hour than the fridge can do by itself.
The thing is, if the soup is properly sterilized, even if it is just refrigerated like usual, the chance of foodborne illness is rare, but it just adds an extra layer of protection. There is plenty of bacteria in the air and on that latel you used.
If you are only making a gallon, I wouldn't go out of my way to ensure FDA standard procedures, but if you have the equipment laying around, it certainly couldn't hurt.