Cfinput With Date Validation - Catch Changes ?

I have a cfform with the following (partial) structure:

Code:

I'm written a simple script that sees if the user has entered a start date in the StartDate field, and automatically populates the EndDate field with that value:

Code:

This script works just fine when entering values directly into the input field. However, it does NOT work when using the Calendar popup that ColdFusion helpfully adds when using date validation. When you click on the calendar icon to the right of the input field, a calendar popup appears; once you click on a date, the date is entered into the field. Unfortunately, JavaScript does not recognize that anything has happened.

This is problematic because the date popup is the easiest way to enter a valid date, and the one that I automatically use, and which I assume that other users will gravitate to as well.