The short answer to this question "Can a 1955 truck be built so that it will handle a trailer like this safely?" is, Yes. First thing to remember is these trucks were made to work. If it's in GOOD original condition to include brakes, steering and suspension then with the right old farmer or old truck driver it'd safely pull your trailer most anywhere in stock condition. At about 45 or 50 mph. The reason I mention experienced drivers is they are not going to overdrive a loaded rig. If they see a vehicle approaching a stop sign, they'll assume it's going to pull out in front of them and approach accordingly. They'll time stop lights so they won't have to stop. They'll allow a lot of stopping distance to the vehicle they're following. You get the idea. I've pulled 16' trailers with my 3600 loaded with 100 bales of hay, total trailer likely 7,000 lbs. But it was on back roads that I might very well not meet a single vehicle on the 12 mile, field to barn trip. This is a stock truck and we only run 30 to 40 mph since it a generally narrow combo paved and gravel road.
So the above said, how and where will you be driving, freeways around Mobile or country two lane roads where 50 mph is fine? Hills or flat country? Is your truck on 12 volts (to actuate electric brakes)? If any of the suspension/steering pieces are less than perfect, make em perfect and you'll be fine. Make the original brakes perfect and install a vacuum booster. If in heavy traffic or hills, front disk brakes shed heat much better than the stock drums and would be a good upgrade. Rearend, the stock unit is likely all you need.
Tongue weight, how much weight will the rear bumper see. In all likelihood you'll want to install a proper receiver hitch or at a minimum have someone with proper skills upgrade the rear bumper.
Engine, a 350 is plenty. Me, I'd go with a bigger than original 6 if upgrading. You likely have a 235 now, a 261 is a perfect upgrade and offers a substantial power upgrade. But that's just me. A much advanced option is a LS engine, quite, great power and fuel efficiency. See
this thread..
Others will join in and you'll get additional opinions.
The driver is a huge part of the equation, upgrading that one part will offset a lot of shortcomings.
Good Luck,
RonR