If we lived in a palace and could only have one friend, we might pick Rajah, too. Jasmine's pet tiger is huge and fierce and ultra-loyal to the princess. His favorite activities include driving off suitors she doesn't like and growling at anyone who makes sexist comments. Looks like Rajah loves smashing the patriarchy, too.
Rajah is kind of a mirror for Jasmine. He can be ferocious or friendly, depending on which person he's dealing with. This is good news for Aladdin. We'd be pretty nervous trying to woo a girl with a pet tiger, too.