Hippogryphs are proud creatures. Very temperamental and protective of their territory. Just make sure you show your respect and take things slowly, and you'll be just fine. Or you can disregard all of that and end up getting a claw in your arm like Malfoy. Whatever you're feeling that day.
Make sure your father hears about this Buckbeak plush! Don't worry, you can just give it a big ol' squeeze without all the theatrics and bowing. Might not give you a ride around Hogwarts, though.