A girl or woman who dances professionally with a ballet is a ballerina. The lead dancer in "The Nutcracker" is a ballerina.
It's more common to call a female dancer a "ballet dancer" than a ballerina these days. Historically, the term ballerina was saved for the very best female solo dancers in a ballet company, similar to the word diva in opera. In French, you call a female dancer a danseuse, and while the word ballerina means "dancing girl" in Italian, it's more accepted to use the word danzatrice in Italy.