I agree with everything Over 59 said above - and would add that I don't think the steel plate would be a good fix on this trailer - that fix was suggested for the 70's trailers that had rear end sag. I think the most likely cause is floor rot (we hope at least) - if the frame is good, then fixing the floor will solve the problem.
Another question - does it have a spare tire hanging on the back - that caused a lot of rear end sag on the 50's trailers.
I echo the advice you got in that if you do get if fixed - keep as much weight off the rear as you can.
1956 Flying Cloud
Four Corners Unit
Albuquerque National Balloon Fiesta
Vintage Trailer Academy - Formerly the original