This is probably more info than you're looking for, but I do have a recommendation to prevent the fridge plug from vibrating loose in the socket (which I guarantee it will do).
I have a dual battery system, with the second battery mounted in the back. The auxiliary battery gets charged by the alternator when the Jeep is running, but when the ignition is off, the auxiliary battery is isolated from the starting battery so the kitchen/fridge can never drain the starting battery.
The auxiliary battery is kept in a tray over the rear inner fender:
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If you have an ARB or Dometic fridge (and some others have this too), the plug on the end of the DC cord comes apart - the "cigar lighter" part comes off, leaving a connector that secures with a threaded sleeve. This is the plug from a Dometic with the cigar lighter tip removed.
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The two-prong plug goes into the outlet pictured below, and the collar around it screws into the socket so the plug cannot vibrate loose. The ARB socket comes with a housing; in the photo below the socket has been removed from the housing and can be installed without the housing if that suits your needs better than using the housing. The ARB sockets with housing are available lots of places for about $12.
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If your fridge does not have a two-part plug like the ARB and Dometic fridges do, ARB sells replacement cords with that plug which you could splice onto your current fridge cord, assuming the fridge end of that cord doesn't fit your fridge.
I've done thousands of road and trail miles with my Trail Kitchen, including camping in the wild in situations where I would not want the fridge to drain the starting battery, so if that's how you plan to use your Jeep and fridge, I highly recommend a dual battery setup with an auxiliary battery for just the campsite accessories.
An added benefit is that in an emergency the auxiliary battery can be used to start the Jeep; I had the starting battery in my JKU fail on a long trip and I've got the same dual battery setup in that Jeep; all I had to do was flip a switch in the dash to use the auxiliary battery as the starting battery. This is the switch in my LJ:
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I also have a solar panel that slides out from under the roof rack to keep the auxiliary battery charged for times when I'm using the fridge but may not be starting the Jeep for a few days; the solar panel keeps up with the kitchen/fridge load and keeps the auxiliary battery charged in most situations.
As I said, more than you probably wanted to know, but I've got years and thousands of trail and road miles of experience in both my LJ and JKU keeping a fridge and campsite accessories charged and operating without risking the starting battery.
And if nothing else I highly recommend the ARB screw-type plug and socket; a cigar-lighter type will let you down someday.