According to the Ramtrucks site, a 1500 Limited with 3.92 rear end can tow 11030 lbs and has a payload of 1490 lbs. Even with my wife and 2 labs in it it looks like plenty of overhead with a 6000 or even 7000 pound trailer if I do all the smart things like WDS and sway control hitch.
What options are you looking to add? All of them will get you closer to GVWR. I recommend going to dealer sites or Autotrader and finding a truck that's as close to what you'd build as you can get. Grab the VIN and plug it in here:
Ram Towing Lookup
I pulled a random VIN for a 23 Limited, and payload was 1120 lbs. I've seen Limiteds below 1k lbs of payload. This is why we ended up with a Laramie instead. We started out with a smaller trailer, but thought we might end up moving up, and we did.
We have 1481 lbs of payload. Our trailer is 5850 dry, but closer to 7400 lbs loaded. With my wife, me, two dogs, and loaded up we're right at GVWR.
If we were doing it again, knowing we'd want to tow our current trailer, I'd have just started in an HD truck. That said, we're full time. Our current setup would be great if we were only towing occasionally, but no way I'd want to be in a loaded Limited with a trailer this size.