Agreed with 392DevilDog. While a 2500 would be better you may not NEED it. I mentioned earlier that I towed my sons brand new 2018 GD Imagine 2670MK with my 2013 1500. My son then bought a 2018 2500 6.4 and towed it about 9000 miles. I went with him on his trip from Pittsburgh to Baytown, TX (1400 miles) and the 6.4 never knew it was there. We got about 8.5 MPG towing it. I also have a 2018 2500 6.4 wiht 4.10's. Mine is loaded except leather, heated seats and sunroof so you can get plenty of luxury options. A diesel is overkill but would work great. And as mentioned, a 2500 Cummins is payload limited also. Payload is calculated by taking GVWR and subtracting curb (base) weight. My payload is 2973lbs (10,000 - curb weight-7027lbs). A Cummins weighs about 900lbs more than a 6.4 so most have about 2100lbs of payload. You would have plenty of room with your current TT but if you ever decide to move up to a 5th wheel then you will be maxing out a 2500 Cummins and likely be over payload.
If you plan on going long distances or towing every weekend you might want to think about a 2500. It will be a much more relaxed trip.
My advice is to load up the truck and trailer as you normally would then head to a CAT scale (most truck stops have them) and get a weight. Be sure you are not over GRAWR. You can find that on that black and silver sticker you posted earlier and should be about 3900lbs. If you are over that then you definitely need to change something. That is a number you want to be sure to stay under. Going over that can cause premature axle wear (bearings, etc). We never weighed my son's 2670 with a 1500 but my step-son has a 2021 GD Imagine 3250BH and he weighed it with his 2020 Tundra and the rear axles was about 400lbs over GRAWR. That TT weighed 9300lbs. I towed it home with my 2500.
Here is the CAT scale slip from my sons 2670MK and his 2500 6.4. He was living in his camper so was loaded pretty heavy. He had 1100lbs tongue weight. With the 3250BH we had 1300lbs tongue weight