You have every right to be concerned about a GA and it was really rude of the Dr to fob you off.
My DS2 had a GA when he was about 18 months old. They let me hold him while they put him under. It was very sudden and kind of shocking. They go so very limp and feel heavier than normal. I was pretty teary when I handed him over but the nurses were really kind and I was beside him in recovery when he woke up. I really believe that it was far more traumatic for me than it was for him.