Hey @AprilGustafson1 !
What process are you using to move the quiz to different courses? From your post, i am not sure if you are currently using Classic or New Quizzes. Either way, you should be able to export the Quiz as a QTI file
How do I export a New Quiz from a course?
How do I export quiz content from a course? (Classic)
And then import the QTI file into other courses
How do I import quizzes from QTI packages?
This should allow you to use the one QTI file that was initially exported to be imported into multiple courses to duplicate the quiz. Once the Initial Quiz is edited for the next day and exported as a QTI file, it should not overwrite any of the previous quizzes that were previously imported.
This may be a few additional steps than just copying a quiz to another course, but it really shouldn't take too long once you get the hang of it.