I have done a lot of this sort of repair on older fiberglass boats, but not specifically trailers, so take my free advice for what it's worth! And there are a lot of ways to do this, but this way works well for me.
The peeling gelcoat needs to be removed, and the chips roughed up with 120 (or so) grit sandpaper. You are looking to get enough scratches that the filler will have a mechanical bond with the scratches from the sanding. It's also important to feather the edges of the chips, so you don't get a hard edge at the end of the filler.
For filler, I would keep it simple and use Bondo. In this small size, it will work well under the topcoat. Mix according to the directions on the can, spread it with one of those little plastic squeegees, sand it down flat, find some pock marks, repeat with a second coat to fill the pockmarks, and sand again. 120 grit is about right for the shaping, if you want to be careful about overshooting on the sanding.
A sanding board is a must, by the way, don't use your fingers to hold the paper! Finish off by moving up to 250 grit. If you have a electric random orbital sander that will help a lot.
For a top coat, the official way is to use gelcoat. Many auto parts stores have small fiberglass repair kits with gel coat, and all marine stores have it. But I have had trouble getting a color match with gel coat. My eye is not that good, and you would need to get a lot of different color gel coat tubes to do this. Also, it ends up shiny and your trailer is not glossy by now. Gloss shows up more than even a poor color match.
What I do, instead, is to use the best quality satin enamel I can find. Sherwin Williams has some that was $30 a gallon 20 years ago, and they color match for free. They also sell in pints. If you apply this paint
in very thin coats with one of those little cat's paw foam rollers, about three coats will cover and you don't need a spray rig. If the coats are heavy, you get bubbles, so keep on rolling until the coat is very thin.
This system worked well on my Tanzer 22 sailboat for five years. We kept it in the water in Portland, OR, all that time, so that's about the harshest test I can imagine. After buffing and waxing it cannot be distinguished from the original gel coat.