Windows Phone 8.1 developer preview is now available however you need to install Preview for Developers app on your Windows Phone first. Note that the update is available for ALL existing Windows Phones 8 running devices including low end phones. The app enables you to receive pre-release OS updates on dev phone, directly from Microsoft! However please note that one of the following three requirements hold true to use this update,

(a) have an active Windows Phone Dev Center account;

(b) have an active App Studio account;

(c) be running a registered developer device (‘dev unlocked’ phone)"

After installing this app, go to Phone Settings > Phone Update and look for updates. Given you're already running latest version of GDR 3, you'll first get a minor update but don't just stop there. Try updating again to get actual 8.1 update which is approximately 500 MB in size.

Happy CORTANA Everyone :)

Edit: 
For Cortana, don't change your region. Simply set US keyboard as your primary keyboard. (After update is installed, change the keyboard and reboot the phone)

Image Courtesy: Joe Belfiore