Mother in Israel,
My daughter had an endoscopy when she was 4 years old to confirm her diagnosis of celiac (had the bloodwork done because she was falling off the growth charts but had no other symptoms). As other posters noted, your baby will have to fast so her procedure will probably be one of the first scheduled for the day. My daughter was given versed and was discharged about half an hour after she woke up. As far as I remember, she did not report any pain, but was hungry afterwards.