My youngest DD had 6 baby teeth removed just before she turned 5 (she is now 6). She has a genetic condition and one of the problems is weak enamel in baby teeth (hopefully her adult teeth will be stronger) and she had two teeth (front one, and one next to it) fused together. She had these 2 teeth out plus 4 back ones.
She was given a GA and they didn't know what work was involved until she was under. When they told me they had removed 6 teeth I was gob-smacked.
One thing to be aware of, the 'wounds' healed really quickly but when we got home from hospital (about 2 hours after the operation) she vomited thick dark red gloopy blood. I panicked and didn't know whether to deal with her or ring the hospital (couldn't do both at the same time).
When she had finished being sick (fairly quickly) I rang the hospital and they said "oh, that is fairly normal, it is only where she has swallowed lots of blood during the operation and it has congealed". Nothing to worry about.
She had the next day off school and then went back.
She then had her one tooth left in the front knocked out in a playground incident but at least she looked symmetrical!
She currently has 2 bottom teeth coming through (growing nicely) but her front teeth are still just gummy! She has already got her year 6 molars (got them when she was 4).
Your DD will be fine, although I found the hardest part was that my DD had to have a pre-anaesthetic sedation before the GA because she was 'playing up' (but the anaesthetist did not know that this was the 4th time she had been under and knew what was going to happen) and when she came round from this she acted like a grumpy drunk. While in hospital, she tried to sit up and banged her head on the metal bedguard and she was more upset about the bump on her head than she was about having her teeth out.