DD had grommits in March (2.4 yrs). No need to take her adenoids out. Like you I've never had a GA and was really nervous on her behalf. Our hospital have morning and afternoon day surgery admissions, we were morning so had to get there at 8am and were gone by about 11am (she was 2nd on list and they did it in reverse age order).
For us the waiting around beforehand was the worst bit - they prepped her for surgery almost as soon as we arrived so she was in her gown - day surgery unit had toys but bring whatever you can to entertain her. She was absolutely fine until the point they told me to pick her up and carry her into theatre - as soon as she saw them pushing her bed off she knew something was up! Obviously younger than yours so understood less what was going on. In theatre I had to put her on my lap and put my arms round her, with two nurses to help me hold her still. The anaethetist did a lot of schtick about ooh, he couldn't blow up the balloon, ooh, mummy couldn't, ooh, could she - I think she was too young and freaked out by the theatre to respond but your daughter may be different.
I won't lie to you - her going under was fairly shocking for me but it's best you are prepared - basically she was struggling and screaming because she was scared and didn't understand what was going on; then the struggling became MORE violent (which was actually good as it's involuntary as the gas kicks in), then the crying turned to whimpering and she was suddenly asleep. What I also wasn't prepared for was the SPEED at which one of the nurses pushed me out of the door (they don't want you to turn around and see them tubing them and obviously want to keep them under for as short a time as possible) - literally about three seconds after she slumped on my lap she'd been taken from me and I was standing on the other side of the closed theatre doors on my own before the day surgery staff got me and told me to go for a cup of tea.
She was away from me for about 40 minutes and they brought her back from recovery when she'd woken up. She was very confused about where she was (the nurses said basically the anaesthetic was still working) and it took about another 40 minutes before she suddenly clicked back to normal, drank ridiculous amounts of squash and umpteen biscuits and DH came to collect us (you have to have two adults for the journey home).
We gave ibroprofen/paracetamol in turns that day and I think one dose the next morning before nursery but she was as right as rain by the afternoon it seemed.
She has no memory of being upset in theatre, this is all wiped by the anaesthetic as well. Even though I was pretty shaken up by the day it was well worth doing - her hearing is considerably better and her speech came on leaps and bounds almost immediately.
As you've said, you can't let your fears show. We just kept saying it was an exciting adventure to tell everyone about. If the grommits need to be replaced or DS needs them I'd be a lot more relaxed just knowing what to expect and being prepared for theatre and when they come round again.