IMHO, prodigies are those children who at a young age can perform at least as well as highly trained adults. So, there has to be talent, drive, family resources, parental attitude, right instructors, etc. Sarah Chang is a prototypical example:

http://en.wikipedia.org/wiki/Sarah_Chang

DD is showing early promises in math and music (learns quickly and naturally and is very driven) but she's certainly not a prodigy.