That's a very short time period for paint to last on metal, even here and near the sea. Preping the surface before painting is as important as the type of paint to prevent rust so I would prepare the surface carefully before painting. If you can, sand blast the rust spots then prep the bare metal, undercoat and final coat. There are a variety of paint prep products made for car restoration. When I was restoring old Brit rustbuckets I used a two step metal prep on bare metal before undercoating and finish coating parts. It's an acid that converts ferrous oxide. You rinse with water before painting. Leaves a fine white powder on the surface when dry.
If you don't want to be repainting every year or so, you should also consider removing all of the old paint over and near the rust spots then treat the metal surface. Wire brushing is ok but a disc sander is better. I used a paint remover made for airplanes that would take anything off. Covering the rust with another coat of paint will only slow the process down.
Cover the edges of the material carefully with paint too. Easiest to do the edges first especially if you are using a roller.
Lastly, dont be afraid to use some paint. Load the brush or roller, dab or roll, then reload the brush or roller. After you have covered a small area, coat it out quickly. If you find yourself rolling a lot or brushing a lot you are probably not using enough paint. I watched a guy paint a neighbor's metal gate and he managed it with one quart !! He'd load a little paint then brush, brush, brush, brush, covering the surface with as thin a layer of paint as possible. If you get a quote from a local that includes paint that's the way it goes. Less paint used more money in the pocket. If your doors show a haze of rust over a large area I would guess there was not much paint on them.
Have fun !!