The all-girl orchestra mentioned by Barbara was Phil Spitalny's All-Girl Orchestra, also known as the Hour of Charm Orchestra. Popular in the 1930s and 40s, it was indeed an all-female orchestra in an era when most orchestra members were male. Most of the members were graduates of music conservatories, such as the Klineberg Conservatory that Barbara and Jason are auditioning to get into.
Barbara's audition piece is from Mozart's "Clarinet Quintet, K. 581."