Two other items actually bother me more. The carport seems like an inappropriate add on, and I find the windows in the bump-out to the right more disrupting than the single window over the portico. Those two windows above the large one seem to be a very contemporary look, and I think of two eyes and a big mouth when I see it. It seems there may be some kind of waste pipe or utility run to the right of the window you're concerned about, so that may be the reason there is no window there. I think you should live with the house for a year and see if there are more pressing issues to put money into before you tackle this one. Shutters definitely aren't the answer.

It's pretty and looks good to my untrained eye!