At 9 weeks old, it is likely this is just playful Doberman puppy and not aggression. It sounds like he is just a normal playful dog. It sounds like you were somewhat unprepared in getting a puppy, especially considering he was a 'present'. Dobermans are far from Chihuahuas and need a lot of mental stimulation and physical exercise (within the boundaries at a young age).
Chihuahuas are generally not 'large dog' breeds. I know my parents Chihuahua hate my Doberman, and he is far less annoying than a mouthy puppy. Also please look into male to male aggression. When Dobermans are mature, they should not live with another male dog. Although the Chihuahuas are small, they have some pretty strong dominant attitudes (in my experience) and can easily push the boundaries of a Male Doberman.
I would really look into getting some professional help, joining a puppy socialization class, and get your puppy enrolled in some formal obedience classes. To me it seems you may be a bit in over your head with this dog, which is not your fault per say, but Dobermans are not particularly suitable for the average first time puppy owner.