Willa - My DS is 8.5 and had his 9th GA on Tues, so we have had lots of practice!
Some points:
You will get a chance to talk to the anaesthetist, and they may give her the choice of brathing in gas through a mask, or having a a cannula in her hand. The EMLA ('magic cream' as it is called in children's wards) will numb her hand, as well as bringing the vein to the surface. They will let you sit with her on your lap, or cuddling her, distract her and get her to look away, and she will barely feel it go in - and it will be momentary. But I would tell her what happens. In fact, what stays in her hand is NOT a needle at all, but a v fine flexible plastic tube. DS has been much calmer since a sensible nurse, removing one once, showed it to him and demonstrated that it was fine and soft and bendy, and not a needle. (though I daresay it goes on through a hollow needle..)
A cannula is quicker and easier than gas for an older child: they whizz it in, then put the anaesthetic down the tube and they are asleep within seconds. Literally, seconds. 5 at most - I would say it took 3 the other day.
Talk to the anaesthetist about pain relief for afterwards: they will probably give some local anaesthetic or some other pain relief while she is asleep that will be working when she comes round.
Yes, you will cry when you leave her unconscious, everyone always does!
At 10 she may be quite low down the list - they do the youngest children first. This doesn't help with the anxiety, and she may hear children crying. The thing is that children can spend quite a time half conscious and half not when they have been brought back, and cry out, It's best not to disturb them too much, and to let them go to sleep and then wake naturally - every time DS has done this he has woken quite calm, and pain-free. But if you can take her into the day room rather than wait oin the ard (tell the nursing staff at the desk where you are) or have her put headphones on and listen to music. On the other hand many toddlers come straight ot of surgery looking fit and keen to climb everest - which could be very re-assuring for her!
Maybe you could talk her through a list of everyone in your family and the GAs they have had, and how they are all fit and well now, and all OK.
Bribery and distraction! I had a series of small treats and distractions for DS which I produced every time he started to get miserable. Again this is good if she is waiting for a long time and the hunger and thirst is upsetting her.
We make a pact with DS, we have 'the last meal' with him, and then tell him we won't eat either, until he is out of surgery, and then we will all eat together. This is a lie, of course, and to keep our strength up we take it in turns to diappear fro a secret snack. Bt do take food for yourself to the hospiatl - but don't eat and drink in front of her whan she is 'nil by mouth'.
DS had a GA on Tuesday for a small operation o the roof of his mouth, and was back at school today, quite happily.
Good luck!