Everyone gets any kind of flying companion for free when they first join and have their character accepted. These can be anything you so wish (yes even little dragons!) so long as they're not monstrous and can't harm another or act as messenger.
Does this mean you can cross a cat with a bird? Sure as heck you can! Flying cats abound!
The possibilities are endless.
Currently only one companion is allowed but there may be another addition of a second in events, but ya didn't hear it from me!