"He Had an Eye for Talent": From the Archives of Paul Mahoney, a "Miss Dallas" You Can't Miss
I'm thinking that this young woman may not be a burlesque dancer at all. Paul Mahoney, in addition to being a professional photographer, also coordinated the Miss Dallas pageants in the 1920s and early 30s. He also "had an eye" for "talent" for Ziegfeld and Hollywood.
I'm willing to bet that this young woman was one of his contestants/discoveries. The pose type is typical of several I saw while looking for information about Mahoney.
There was no Etier family in Dallas from 1920 through about 1935, which complicates matters. However, several of the articles about Mahoney and the Miss Dallas contest indicated that the contest was won by women from surrounding communities, so she could have come from the "suburbs."
There was a Lillie May Etier, age 9, who was living with her family in the Lagow area of Dallas County in the 1910 census. Presuming, of course, that the family stayed in the area, this would make her the right age to potentially be one of Mahoney's contestants in the 1920s.