Check the book by Mary Lou Widmer entitled Margaret, Friend of Orphans. I can tell you that the Female Asylum was located on Clio St. in New Orleans, that it closed in 1938, and was torn down in 1966.
When the girls reached a certain age they were transferred to St. Elizabeth's on Napoleon Ave., which was later purchased by Ann Rice and today has been renovated into condominiums.
If you will check the online records of the New Orleans Public Library you will find a wealth of information.
W. H. Cook