I’m with Grit Dog on this. That F350 is plenty of truck for the job, but before taking off on a long trip with that much weight you’d be wise to get the transmission built, and I DON’T mean rebuilt stock, I mean “built” to high performance standards.
A few tweaks to the motor would help too. You don’t need to get crazy about it but a little more power would make it nicer. It’s there for the taking with a few minor mods.
That’s an excellent truck to work with.
But - expecting a high mileage older rig to do a reliable job towing heavy without going through it first is risky, doesn’t matter what brand.