D.K.
Just let her know that she'll be asleep for the whole thing and will have medicine to make her feel better afterward. Also tell her that she'll be on a special diet afterward. VERY special in fact, meaning ice-cream, jello, mashed potatos etc...
I don't know if she's the type that this works well with, but my son always feels better once he has all of the details of something and if I can give him the pros and cons and do it all in a matter-of-fact way that makes it something normal and yes maybe annoying, but necessary. He usually agrees that it's the right thing and I made the right decision. So you might try telling her why it's necessary, and why it should be done sooner rather than later. I had mine out when I was 18 and it was HORRIBLE, but my mom said it barely bothered my brother to have his out when he was about 8. The doctor agreed that the older they get, the harder it is. Kids heal so much faster, so the earlier you get this done, the easier her recovery will be.
Anyways, I know this wasn't too much help, but maybe there's something useful in here. :) Best of luck!
BTW: I agree with the other mom that said that the recovery pain after the surgery isn't anywhere near as bad as tonsilitis, so it's this manageable recovery pain once, or keep getting tonsilitis a few times a year forever.