Somebody posted this picture (please follow the link; Shorpy asks that we link rather than grabbing pictures. I'll comply even if somebody else didn't) on a 1920's Facebook page last night. It's not from the 1920's, but whatever.
I thought the girl looked familiar--it's Billie Burke, the silent film and stage actress. Or Glinda the Good Witch from The Wizard of Oz. I haven't found any information online about her ever having been a nurse so I assume this is a promotional shot for one of her stage roles (she didn't make any films between 1916 and 1920).
I thought the dress looked familiar, too--it's pretty much Past Patterns 7986 (again, please follow the link. The image isn't mine). This dress seems to be somewhere on the progression between full-cover apron and housedress. I can't say it was ever really used as a nurse's uniform but it's at least plausible (the cuffs and probably the collar should have been removable).