My sons time having it brought up by another child.

My sons time having it brought up by another child. My son is six years old. He is an only child and is absolutely perfect in every way. He has been stuttering for a while, but his kindergarten teacher said “don’t worry about it”. Well, it’s starting to get worse. It normally happens when he starts a sentence by saying “I I I I love pizza”( or something like that. Today was the first day another child brought it up. A kid who probably didn’t mean to hurt his feelings asked him about it. He brushed it off, but brought it up later and it clearly hurt him. School is about to start up and my wife and I will be looking for a speech pathologist. I’m looking for advice from people who have been in his shoes. Other than loving him unconditionally and always supporting him, what can I do to help him. My only goal in life is to make sure he is happy and lives his life to the fullest. Please, help me be the best dad possible, how can I help him?