Tow vehicle advice

The mid-size pickups can handle it, with the caveat that you plan on driving about 60 mph (not much faster) most of the time, and in the mountains drive 35-40 mph up the long uphill grades. If you want to run around faster than that (and use more fuel) then the 2.7L turbo F150 or 3L Ram turbodiesel will be more satisfying. Not just stronger engines in the larger pickups, but more cooling capacity and heavier duty transmissions, too. But yes, the mid size pickups can do it if you don't push them hard all the time. Realize that you're dragging a huge sail behind you, and a small increase in highway speed causes a large increase in power consumption. (BTW, non-turbos lose something like 2% of their HP for every 1000' of elevation gain, so turbos have an advantage in the mountains where you need power the most.)

Personally, I would want at least 1000 lbs of listed cargo capacity (CCC). Water is 8.3 lbs/gallon, and you'll have 6 gallons in the water heater. If you fill the fresh tank, that's another 300 lbs. Add in LP, battery, and gear. Be sure to locate and look at the actual-weight sticker (usually inside a cupboard door) of the unit you're thinking of taking possession of, to see what CCC you really have after all options, then add the weight of the other items mentioned above to get a better picture. And all that will be riding on a single pair of tires; check the load capacity of those on the TT.

Not trying to discourage you, but go in with both eyes open and well armed with info.

Jim, just get the half ton now. We got our half ton (11,200 pound towing limit) when we were at 3500 pounds loaded. It was a beautiful experience....truly stress free towing. We moved up to 7k pounds after two years and didn't have to change the truck. Saved us many thousands and the hassle of changing. My personal rule is not to exceed 60% of max towing. More margin than most recommend.

I don't know what payload numbers are like between the mids and the half tons? If it buys you a few hundred pounds more (sure it does), that would be very, very nice too.

Are you always going to have a 19 foot trailer? I would at least consider a 1/2 ton pickup.

Any of those smaller trucks will pull that trailer but will they carry you, DW, your stuff, the tongue weight and hitch? Payload issues are more important than “will it pull?”

That’s good to get the truck for the trailer you’re intending to tow but you may want to think about your next RV too. Many RV’rs upgrade after a few years for many reasons so if you can, I’d suggest one ton or something similar. It’d give you plenty of capacity now and for any upgrade you’ll probably do later. The immediate benefits is a much better towing experience.

Any of the mid size trucks and even some SUV's would be well capable.
The only other thing you may want to consider is the likelihood of wanting a larger unit in the future, If so, you may want to look at a regular half ton truck F-150/or a 1500 series.
Just looked at the specs on that one. If you are looking at a cross country trip, think about the CCC, Less than 800 lbs on that model, and remember propane tank, battery, and water all count against that number.
You will probably have to tyravel with empty tanks and pack light.

If it really weighs 4,000 pounds loaded then any of those compact trucks should pull it. Don't forget water in the fresh tank, water heater, and waste tanks in your calculations. Also propane and batteries are normally not included in the dry weight.
In my opinion you will be much happier with a full size truck. They are more plentiful if looking for used vehicles. They will do a better job of towing, offer more interior room, and get basically the same fuel mileage when towing.