Is $1,150 to install a new outlet with a dedicated circuit for a window AC unit a fair price?

I live in a 2-story century home in Chicago that gets very hot upstairs, especially this summer. My current AC unit is about 15 years old and struggles to cool the upstairs, though it cools the first floor and basement well. I want to add a window AC unit to my bedroom, but existing outlets are too far, and the AC unit's cord is only 6ft, with the manual advising against extension cords. There's an old, non-live junction box under the window. I'm debating if a dedicated circuit is necessary since I plan to use the window AC sparingly, mainly on hot nights when sleeping, and if the cost is justified for such limited use.