This is the song which plays while Lorelai and Emily do their turn on the catwalk.
Girls Just Want to Have Fun was written and first recorded by Robert Hazard in 1979, but is best known for the version performed by Cyndi Lauper, released as the lead single from her 1983 debut album, She’s So Unusual. It became her breakthrough hit, signature song, and a feminist anthem, reaching #2 on the charts, and promoted by a quirky, Grammy-winning music video.
The song describes a girl or young woman telling her parents that she needs to have some fun in her life in order to express herself. It’s something that Lorelai would have wanted to say to Emily and Richard when she was growing up, so the song must have resonated with her. Lorelai later says she chose all the music for the fashion show, and the chances are very high that this song is in her personal music collection.
(Note that Cyndi Lauper wears a red dress on the record cover and in the music video, just like Lorelai and Emily!).