This is one of the later Vitaphone shorts--known as a "Melody Master". These later musical shorts generally were more straight forward and had simpler sets and no real story to tie it all together--just a famous band of the day doing their stuff.
"Frances Carroll & 'The Coquettes'" is a very unusual short because it's the only one I've seen featuring an all-girl band. I am sure Vitaphone might have made more films like this, it's not the only one in the mega-set (with 11 hours of their musical shorts) with a ladies' band--there's also "Rita Rio and Her Orchestra"--one that is later on this same disc.
The short features singing and dancing by the elegant Carroll, a wild drum solo and some tap dancing that was fused with ballet by Eunice Healy. It's interesting that unlike her male counterparts, Carroll seemed to be selling sex, as the way she danced about while the band played was nothing like what you'd see the guys doing with their bands. But, even without this, her band was quite good--and very intense. I liked their fast swing style--it was very catchy and toe-tapping.