It always takes longer than they say, so don't panic when they take her in late and run over their estimated time.
When she goes to sleep she may get very floppy quite suddenly (mid verse of a song if she's like my DD!) so if she's on your knee or you're supporting her be aware you may need a quick catch reflex
.
They will bundle you out of the anaesthetic room very fast whilst fussing over her once she goes over, that is completely normal although it seems odd the first time you see it. Sometimes they can do a couple of odd twitchy movements as they fall asleep, again totally normal although it probably won't happen.
She may be able to cuddle a special toy in the anaesthetic room which in a lot of places they will hang onto and pop back in her arms before she wakes up so make sue you bring one.
When she does wake up she may be a bit fuddled or weepy or very VERY angry about everything including the colour of the curtains. It's a completely normal side effect of the gas and wears off after an hour or so.
Try not to worry, planned ops like this are incredibly safe. I've lost count of the number of anaesthetics my DD has had now and although it's not nice for the parent as far as they're concerned it's not bad at all. I wasn't ever very good at reading while waiting but a trip to the cafe for some sweet tea and a chat to someone, even on the phone worked wonders.
Wishing you all the best, it's a horrid thing but it'll probably go way faster and better than you're expecting.