When my son had his hernia surgery (outpatient, right inguineal hydrocele - in the groin) I was a nervous wreck, but at least I didn't have to see him get stuck at all.
They let me hold him while they gave him a sedative that would make him fall asleep. Once he was pretty out of it, then that is when they took him back for the prep and surgery, so he didn't even know they were sticking him at all.
Since they are already going to put them out, they told me they wait until they are already under the gas before they even place the IV so the baby doesn't know what happened, and they don't have to deal with a squirming, screaming baby - AND they are more likely to get the IV placed right the first time without having to stick them more than once.
When he started to come around, they let me go right back in and he did have the IV still in his arm, but that wasn't a big deal as it was already there.
Good luck with the surgery - I'm sure she will be just fine. I was in absolute terror to let him go back under the anesthesia, but he came through great and we were home with him and he was running around like nothing happened by lunch time that same day.