As Quattro says, it’s worth using a rust converter to neutralise any corrosion. If you’ve caught it soon enough, you should be able to stop it getting any worse, and it will last for a good few years.
Definitely, it’s a good idea to check over the rest of the car throughly before getting too stuck into one area, if you’re not sure what else you find. Also, whether you can or can’t weld, and how much of a project you want will influence how throughly you want to prod at that area. If you’re paying someone to do the work, it’s usually best to replace larger areas, or complete panels to original seams. In which case, it doesn’t really matter whether you have one hole or lots in a given area. The cost is similar, until the repair spreads to the next panel.
If you want to go further, I’d start by removing anything flaking, or anything that comes off easily by scraping, and keep going until it’s not easy to flake off. Chip off any “metal” that’s started to corrode into laminates. Gentle tapping with a hammer, or scraping at it with a screwdriver will find anything that’s no-longer sound. Be prepared for this to uncover much more than you can first see though.
If the original coating is no longer properly adhering to the base metal, it actually makes things corrode faster than if they were just left bare. Unfortunately if you find holes, then the only way to properly sort it is to cut out the bad metal and replace with new. By the time the first hole appears, it’s usually paper thin over a much larger area, and trying to weld up just the hole never works.