Hmm- a lot of people will argue with me on this, but I think "I Know Things Now" from Into The Woods might work well. I've never heard her sing, so I wouldn't really know, but a lot of my friends (myself included) who don't have a great range can sing it decently. And it's a fun song, too, and Little Red sings it in what I think is an obnoxious voice, lol, so she can have fun with it.
A most ingenious paradox.