Doodle is the hero of Brother's memory. In Brother's mind, Doodle can do no wrong. Most readers feel lots of sympathy for Doodle and want to see things turn out well for him. Because he's so vulnerable, readers might feel protective of him. Suspense over what will happen to him is a big part of what keeps readers reading to the end.
Brother is the narrator of the story and he fits the bill for protagonist in a few ways. Importantly, he's the driver of the action. He's the one that pushes Doodle to go outside and learn to walk. Eventually, he also pushes Doodle a bit too hard, and Doodle dies. Though Doodle may be the hero of Brother's story, Brother is the character that pushes the story forward. He's also a character we can sympathize with, as he struggles with his feelings of guilt.