Moving it a few miles would probably be ok. Texas too Alberta! Wow. I towed a Dodge D150 behind mine on a car trailer for about 10 miles on back roads. That with the weight of the trailer was probably about 6000lbs. I have the 292 and a four speed with 3.89 gears. Pulling it up to speed was no issue at all. Stopping was a real PIA. Long planed braking and down shifting. Trailer brakes would have helped.
After about 10 years of pounding around with various F150s with 300/4.9 sixes I finaly realized that I need more truck. Coming in to the scales at 15k with a half ton pickup made people raise their eyebrows. The found it amazing that I used a six cyl engine to pull with too. I got tired of fighting sway and headwinds at 45 mph and winding out in third going up hills at 35 mph. I broke down and bought a massive gas pig F350 V10. Now I don't even have to worry about hills and wind and sway.............Just rather or not I will make it to the next gas station.
I do miss my old straight six four speed trucks. If I could find a nice 75-96 F250 or F350 set up like that I would get rid of this gas pig in a heartbeat. Problom is that all those types of trucks were sold to commercial and government users and ran in to the ground.
If you had a F350 I would say go for it. The big brakes and deep gears would probably work fine with a bit of effort up and down hills. But based on the bit of towing I have used my 64 for I would limit it to about 3500lbs or so and even at that number trailer brakes would be great. Your truck will move that camper. Just not stop it worth a shart and going up hills will take a long time in second gear.
Boss, We all have a right to be stoopid if we choose to be, you are talking about using a 50+ year old truck with the smallest engine available make a 2000 +/- trip one way through the hill country side of this continent, grab a travel trailer and drag it back home.
Why don't you rent a truck or van to make that long trip with? Once you have it home then take it out on a 50 mile camping trip until you get a better feel for what your truck is capable of doing.