The dress is beautiful! I agree with analise that you will probably be the best dressed woman there, but I have gone to shows recently (especially Sat eve performances) where some people have been dressed more formally (men in suits and women, especially younger ladies, in fancy long dresses).
When I see them, I always figure they have a much more exciting life than me!
I try not to dress down too much for the theatre, but honestly, if I've been walking around Manhattan all day, and especially if it's the summer, I have a tendency to be much more casual. Not fun to spend the day walking through midtown in 3 inch heels.
Have a great time.... I just saw Phantom for the second time. Took my kids, they loved it (they are 15 and 11). If you can, get the soundtrack beforehand so you can familiarize yourself with all of the great music.