We have a Keystone Passport Ultra-lite 26 ft bunkhouse. Dry weight is around 5300 lbs. Loaded is probably around 6000ish.
Vehicle is 2017 XLT non-EL with HD tow. The power of the vehicles is great. The trailer brake controller is AWESOME.
I did experience more sway and body roll with the vehicle and trailer than I liked the first time I towed. I added some Sumo Springs that helped a lot. (See my write up in the Towing and Hauling section in the thread Suspension enhancements for sagging.)
A properly setup WD hitch and sway control are a must. I have used the chain type with the separate sway control and the type that use the bar type that slide on the bracket as integrated sway control. Both have pros and cons. So to each his own on that.
I have always used the 85% rule. Meaning I try to keep the total load at 85% of the max rating of the vehicle. This gives me a little internal comfort that I am not at the max or on the edge of safety. A vehicle's rating is based on many different things, not just "go and whoa". There is the obvious of moving and stopping, but then there is the moving and stopping on hills, in corners, on rough ground, and many other scenarios. There are suspension components in the front and back that get loaded and bound up in odd scenarios. And so much more.
Most vehicles can move more than they can safely make a trip with (Toyota shuttle commercial - it was moving in a straight line at 5mph).
Also I have read that some states can and will check vehicles to makes sure they are not overloaded based on the door rating.
Tire pressure is a must to check on the towing vehicle and on the trailer. In my experience the 35psi to daily drive on is not enough to tow with. I usually put the trailer at 48 of max 50. I put the vehicle at 40 of max 44.
How you load the trailer and vehicle needs to be considered. Once you get the rig setup like you like it and it tows well, remember how it was all loaded and keep it that way. Moving a few hundred pounds from front to rear or visa versa can impact the towing characteristics.
Tandem axle is more stable than single axle.
The longer the trailer the more sway you will have, generically speaking.
Like the one person said, renting something for a weekend to try is a good idea. Some places might even let you tow a few campers down the road from their used lot to give you an idea of what to expect.