looking at the clues the other three users have provided to me. "no Jane" = she is no average ordinary girl. She is a society girl. the best clue being provided by Jeffrey who gave the books title as "the last of the bells. belles are society girls.
from amazon books google search.
Inspired by Fitzgerald’s own courtship of his future wife Zelda, ‘The Last of the Belles’ centres on the Southern beauty Ailie Calhoun from Tarleton, Georgia, who finds herself the object of attention of all the officers at a nearby army base, including the narrator, Andy. A wistful and melancholy exploration of unfulfilled dreams and lost youth, the story is considered one of Fitzgerald’s finest pieces of short fiction.
a beautiful girl or woman, especially the most beautiful at a particular event.
the term was often used amongst high society people at their grand balls.