I've got one just like her.
She was terrified of the Snow White ride and to this day will not watch Snow White anymore because of that ride. She also refuses to go back on Winnie the Pooh because of the storm.
But she absolutely LOVES Goofy's Barnstormer. This was her very first roller coaster when she was your daughter's age. We weren't really sure about whether she would like it, but after one ride, she was HOOKED. Now when we go, that is one of the rides we have to go on over and over again, along with Test Track and Thunder Mountain, but that's another story.
Goofy's Barnstormer is perfect for a first time coaster, because the ride itself is very short. I mean, like MAYBE about 1 minute, if that. Actually, it feels more like about 45 seconds to me.

But it's great because if she doesn't like it, it won't be long before it's over. I don't think you'll have to worry about that though, because it is so much fun. It's all outdoors, and there's nothing major, just a few little short drops and a couple of twists and turns, but it is a fun little ride.
Have a blast!