The professor is mostly right, but it's not a simple right-or-wrong situation.
"Windowed" is most commonly an adjective. A "windowed shed" is a shed that has windows. However, some dictionaries do also list "window" as a verb (whose past form is "windowed"), with meanings "to furnish with windows" or "to place (something) in a window."
"Door" can also be found as a verb in some dictionaries, but not meaning "to furnish with doors"; rather, it is commonly used by cyclists to mean the act of running into a car door.
However, there is a linguistic process called verbification whereby new verbs can emerge in popular usage from nouns with a related meaning. It is part of a larger process called "conversion" and it's happening all the time in English. For example, "email" was first a noun, but has emerged as a verb: "I emailed you."
While I don't think I've heard anyone talk about "dooring" or "windowing" their house, I immediately understand the meaning, and it doesn't sound terribly bizarre because most English speakers are used to verbification.
In summary, what you wrote is likely to be understood, but to be strictly correct you should say "installing doors and windows" (or having them installed, etc.).