i have seen first hand, lots of kids under three, at ANgelina Ballerina (20mins performance, interval, 20mins performance) and The Gruffalo's Child (similar) = the kids under three didn't cope very well. The babies were fine, but the toddlers got distressed, no matter how great the music was, entertaining the show was.

Annie is a much longer show. I would not take a two year old, i would worry that you and your child would both end up missing the show. A professional show like that, the lights will be down for the audience, many little children find the audience in dark, a bit scary.

only my opinion, you know your child better than anyone else.