I am doing a very large project for hotel reservations, and I can tell you that if you use JS dates, your problems have not even begun. Just wait until you run into the problem that people in different time zones start feeding dates into your db, it will drive you half nuts.
I do not know if this will also be your problem, but using strings as a date is really not a bad idea, because they are constant, not relative (JS dates are calculated from GMT +0:00:000).
The only thing you must do is NOT store them as MM/DD/YYYY but as YYYYMMDD. That way they sort properly.