Small white dog (probably beagle) with spectacles and red tie.
Mr. Peabody, as noted, is smarter than any living being on Earth. He is devoted to Sherman and has accomplished tons of things in life including inventing zumba, the fist bump, and winning the Nobel prize many times. He looks out for Sherman and does not want bad things to happen to him. His intelligence has time and again saved him as he is able to think about his situations and the best solution to get out of his predicaments while keeping a calm head, regardless of how dire the situation might be.
However, despite his intelligence or perhaps because of it, he can be inept about the delicacy and bonds of family. While he does display an understanding of how to be social as he often invites important people like the president over for dinner and was able to quickly charm over Penny's parents, his relationship with Sherman is not that simple. He in some ways seems to see children as part of a project or an invention where the parent builds and raises the child, but cannot understand Sherman because of this, as he wishes he wouldn't grow up and would always listen to his orders and having to be told by Leonardo that children are not like inventions because they are individuals who grow up, have their own opinions, and will spread their wings. This scares Mr. Peabody as he does not want to grow distant to Sherman, which is possibly the reason why he always tells Sherman what to do, to make sure he is not in danger but also to secure the bond he has with him.
However, through his misadventures with him and Penny, he realizes he must grow to respect Sherman's growing sense of independence and that no matter what happens, the bond between them will never break. He also has a habit of trying to act cool and saying terrible puns he thinks is funny.
He is normally a very patient individual who takes pride in himself and his accomplishments but will be tolerant of people who look down on him and try to show them what he is capable of, though people like Ms. Grunion will push his buttons. Additionally, while his intelligence prevents him from normally resorting to his more primal, animal side (as shown when he refused to play catch the stick), he does sometimes resort to his canine tendencies as shown when Sherman threw a ball and Mr. Peabody eagerly chased after it. His more vicious, "dog" like behavior will also subconsciously emerge when those close to him are injured or in danger, as shown when he saw Ms. Grunion try to take Sherman away, he cried it hurt and begged Mr. Peabody to help, and Mr. Peabody temporarily reverted to being a dog and proceeded to bite Ms. Grunion in anger, much to his own horror. This shows he is protective of those he loves.
In the show, Peabody was snobby and treated Sherman like a pet and an underling than a son.