I’m going to assume you mean a deserted island with electricity and an internet connection, otherwise bringing a computer or a movie would be useless.
Pet: My cat Camille, because she is the sweetest kitty in the entire world.
Computer: My laptop, because it has all my stuff on it.
Book: That’s a threeway tossup between One Hundred Years of Solitude by Gabriel Garcia Marquez, The General With His Labyrinth by Gabriel Garcia Marquez, and Palomar by Gilberto Hernandez. But if I really had to only pick one, I would go with Palomar because the combination of words and pictures is beautiful and it has a great rereadability factor.
Movie: I consider The Lord of The Rings to be one great big movie and I would bring the Extended Version. 12 Hours of Majestic Epicness.