Okay, first I want to say maybe you should find another vet. Part of their job is to reassure you that your dog is in good hands.
Secondly, don't worry. Dogs as small as yours get fixed everyday. Lola was spayed on Friday. Not just spayed, but she had eighteen extractions and she was microchipped. I was a nervous wreck too. She was out of it for a couple days, but now she is pretty much back to normal. By the way Lola is only 2lbs 10 ozs.
Your little one will be fine. Keep us posted.