They can paint match local spots, but depending on how old your paint is, it will never look right and will always be noticeable to you. Even painting the door would make it stand out (potentially) from the rest of the car.
You could find touch up paint, and it will be the cheapest route and look about the same if you prep the area well (as in sand it, smooth it, and put on a layer of primer, then paint). The rust you are seeing is flash rusting, it will probably come off with a very light sanding, so no worries there.
Brave man letting your Z brave Andrea (don't know how bad you got it in orlando). My ZX had a lake in the driver side when it stopped raining.