I just went through this myself. I was looking for a 4wd Big Horn 1500 with a 5.7 and 331 rear end and factory brake controller to tow our Grand Design 22mle TT. I found a very nice 2017 quad cab that I'm really happy with.
To find your specs, you can use this vin lookup tool but it's only going to work with 21+ model year trucks:
Explore the Ram Trucks towing & payload capacity guide. Find information like Ram 1500 towing capacity, Ram 2500 towing capacity, payload specs & more here.
www.ramtrucks.com
I used a combination of other things to narrow my choices. Pic of the tailgate will tell you 2 or 4wd. Interior pics of the dash will show you if it has the factory brake controller. In most cases, if it has this, it was ordered with the heavy duty towing package and came with the 392 rear, but not always (like mine). If looking at dealers pages, they will often have a free link to the Carfax. Carfax will show you the original window sticker, where you can see what options it came with. You may also be able to find a build sheet online using the vin. If you have the truck year, style and options, you can look up a tow and load rating for the truck on one of Rams published tables for that year and find the specifics for your truck. As others mentioned, you'll run out of payload before you run out of tow rating.
A couple of things concerning your trailer. With the GVWR of 7100 you're pretty much within the limits of just about any of the 1500's. I'm not convinced you even need the 392 rear. As a daily driver, then you'll effectively have one gear higher than if you had the 392 and you'll likely get better mileage on the highway, at least. Both axle ratios will have the same payload, fwiw. Just some thoughts I went through when I was looking recently.