@HumuHumu
Please redeem the NOT Uplay key from here:
http://tomclancy-thedivision.ubi.com/game/en-GB/beta/index.aspx

Further down the page, you'll find a button called "Redeem your key" or similar. That's where you can enter the key. Once you've done that, you'll have to wait for Ubisoft to apply Hazmat to your Uplay account.