You can locate your license information on the NYS Education Department website at  Select "Veterinarian" in the list of professions contained in the first box at the top of the page, and then enter your name in the field just under the box.  Click on SEARCH, and then click on the license number that should appear to the left of your name.

Among the items listed, you'll see "Registered through last day of:" - this is when your license to practice is due to expire.