Well, sounds like you are off to agreat start. You could take it to a sandblasting/paint shop to go over the spots (or you could do it yourself if you know how to do it) then prime it, and repaint it. I think there is a primer that has rust inhibitor of some sort (been awhile and I m not sure we used it) but paint places will have it.Not a rust expert by ANY means!! Very interested in this, love my trailer but this is an issue for sure!
It's really not a big deal, I swear. I just use a dremel to sand them down to bare metal and spray clear rustoleum on top to protect it. If it's an easy to match color like white, you could use the white instead -- mine is bright blue, so I don't try, LOL. A little bare patch here and there doesn't bother me.
I also only mess with it if it is a damaged area (a farm worker hit one of my stock side panels with an implement, sigh). Small patches of surface rust don't bother and aren't a big deal. I just keep an eye on them and run a finger over them to feel them out now and again. But it really is pretty simple and I LOVE me some steel any day!
Sand, rustoleum, and if you are worried, repaint over that. Sanding down is the really key part of that. If you're talking surface rust on flat areas, this is easy and painless, but you do have to keep on top of it. Make sure you also get rustoleum into the parts that are rusty - I have found that the aerosol cans of it don't do nearly as nice a job as the jugs of it you can paint on yourself.
I have a 1980 Kingston that I used to spend hours and hours and HOURS on each spring, and last year I just gave up. Until my trailer guy tells me I need to do something about a particular spot, I just leave it alone. I'm letting it go slowly and gracefully and saving the money and energy by saving for a new trailer.