I don't see any worries, cute pup. Nothing like a boy and his dog. Hope he's walking him? Your son looks to be the right age to to have a pup and the responsibility with supervision.
I think you made the right choose. You reacting immediately was great, you have a 3 second window to react and show her that you are the boss, don't stop, and enforce that same thing to your son, so he is above her too. If everyone in the house don't do the same thing, you will have what I have...