According to the American Kennel Club, "The Am Staff is a people-oriented dog that thrives when he is made part of the family and given a job to do. Although friendly, this breed is loyal to his own family."
Regardless of the breed, if a dog is raised in a home full of love and treated with care it will reflect that behaviour to it's people.
Much of a dogs behaviour is instinctive - behaviour reinforced by generations of survival, albeit closely tied to human assistance.
A part of a dog's natural behaviour is to take an active role in the protection of the pack. In the case of a dog that is a part of a family of humans, the pack is the people in the human family.
A dog attempting to achieve dominance would most likely demonstrate a number of behaviours that would likely concern you over a period of time. Not all dominance-driven behaviours would be aggressive however, so it would be appropriate for you to continue to watch your dog closely. One of the most obvious that comes to mind is the dog not allowing other trusted family members to come near your two year old at nap or bed time.
There is a lot of written information about dog behaviour and in particular behaviour that is intended to achieve dominance.
Based on the information you have provided, the behaviour you suggest is unlikely to be an effort by the dog to achieve dominance.
Hope this helps.
"Get to Know the American Staffordshire Terrier", 'The American Kennel Club' website, retrieved 29 May 2014.
"American Staffordshire Terrier Page", 'The American Kennel Club' website, retrieved 2013-06-16.lj