O.D.
I would go to another dentist. My kids go to a pediatric dentis and she has never suggested total aneshesia. My little one who was 5 at the time, had a few cavities for which we had to go 3-4 times and each time she had local anesthesia. When one molar got infected, we tried fixing it and even then, only local anesthesia was done. The molar got infected again so they had to pull it out. Local anesthesia was used and there was no problem.
I would not go for general anesthesia. It is risky. Even for adults, total anesthesia is risky. Imagine for the little ones. Try to get another dentist and see if you can do it with local anesthesia and maybe laughing gas.