Good idea. I had never heard of sleep inertia, but it makes sense.
Now I'm not sure about recording dreams. Is it associated with REM? If so, then recording it would be beneficial to track the strength/duration of REM. Othewise, dreams by themselves are simply our minds trying to work out problems. As Freud put it, they often display our repressed desires.
Scale of 1-10 would be too ambiguous. At least 1-5 doesn't include too many choices and thus the results can be consistent. Keep in mind that I could use decimal places, negative numbers, and numbers beyond five, which would be off the scale and might be encountered when something extreme is done (no sleep for 2 days, etc.)