Redfish,
I did that to my utility trailer back about 10 years ago. I bought a 2000 lbs capacity 4X8' utility trailer that bolted togethe. I welded on side rails and instead of a plywoood floor I installed pressure treated 2X6 lumber, all drilled and bolted down. A few weeks after the trailer was finished I noticed a light coat of rust all over the welds and the angle iron side rails I added.
I found a paint on product that you just spread on with a brush after you wirebrushed any loose rust. The coating goes on clear and almost immediately turns black as it converts the rust to a paintable surface and needs no primer. I finished the job with a few cans of black spray paint and 10 years later, the trailer still does not show any traces of rust.
Unfortunately, I don't know the name of the product but you do not have to dip the whole trailer? Just paint it on the rust and when it dries, paint over with the color of your choice
Look in some of your local Hardware stores....I think Rustoleum makes a rust converter, but I', not sure if that's the brand I used....but they are all about the same.
...Rich