I would think a seven year old with fears would be tricky. I watched the thing being built for three years and I'm now 44 years old and had to talk myself into going on it. I loved it and I hate roller coasters. One hint - do NOT let your daughter see the outside of it. The climb to the top and the "plunge" look a heck of a lot worse than they are.
For a roller coaster wimp, this tops everything at Disney World except for Twilight Zone (still gets me with the mind games). I wouldn't force the issue - let her decide. It's not a stressful ride at all. I wouldn't be going back this weekend to hopefully ride it again if I freaked out. And that is from someone who can't handle a ferris wheel.