Additional info that may or may not be relevant:
-This sickness is going through campus, so it's not out of the blue (I have like, a ~1500 person campus, not hard to get sick here)
-I don't seem to have a fever anymore, but I have what seems to be an awful head cold and it's hard for me to stay awake for more than ~5 hours.
-The professor is super nice... but I don't really know her at all.
-I've gotten 4/4 on all of my mini-assignments thus far, participate in class, etc.
Would it be totally out of line to go to the professor's office early tomorrow morning and ask for a one day extension?
ETA: The syllabus merely says this of late assignments, "Note: Late submissions must be prearranged with the instructor."