Look for the Silver Lining (1949)

After getting her start in her parents' vaudeville act, Marilyn Miller is taken under the wing of dance sensation Jack Donahue. He senses the girl's enormous talent, and before long she's performing on Broadway. There, she is extremely successful and finds love with songwriter Frank Carter. Yet obstacles remain for the rising star, especially when he proposes marriage just before he's set to be deployed in World War I.