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Chances are that rust goes a lot further than what is visible. Only way is to start sanding and see where the rust stops and clean metal starts. Pull off the interior door panel and see if its rusty on the inside as well.
You'll have to cut out the rusty area and replace it with fresh sheet metal. Or just replace the door with a used one.
If you're too shy to weld in new metal, you can also remove the door handle, grind down the surface with a sander, bondo over it good and smooth, and then paint over it as advised.
Lack brings up a good point that you should look inside the door for rust on the inside. That rust looks pretty bad.
I just fixed this on my own (luckily I caught it much earlier).
You need to open the door panel and a take a look.
There is a metal backing plate right behind that rust on the inside. It catches moisture that works its way in from around the door handle on the outside, as well as dripping/drainage happening on the window surface. If your lucky, the rust will be fairly contained to the edge of that backing plate. However, make sure to order replacement handles before trying to take the old one off. Because the bolt that holds that handle on is probably toast, and it will snap as soon as your try to loose the nut that is holding it to the door.
If the rust is fairly contained on the inside, you could follow some of the advice given in the prior posts (basically do the small amount of body work on your own). Or deliver it to a local body shop with the door and handle already off, and they can probably clean it up and paint it at a very reasonable rate (that's a relatively easy area and surface for them to work on, and if the door is already pulled apart, its even less tedious).