Navel looking clothing was the style.
The arm patch is the style of a Navy Chief’s chevron. Single star would be a Senior Chief.
Was there something like the “sea scouts” during World War I? She was a little young to be a chief petty officer in the Navy. BTW, the quality of the old black and white portraits are great.
Might not be her uniform (especially if she’s 14 and given the insignia), she might have had somebody special in the Navy (this was during World War I given the dates you posted) and took a picture wearing his shirt for him.
Compare w WWI Navy Nurse uniform.
Time traveller?
Google for images of "WWI Navy Nurse uniform".
I searched around, and found that insignia with “Sea Cadet Chief Petty Officer”.
http://benmoreellseacadets.weebly.com/all-about-the-ranks.html
Anoreth the time traveler?
Search this web site for the insignia she has on her sleeve:
http://www.uniforminsignia.org/index.php?option=com_insigniasearch&view=insigniasearch&Itemid=53
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
(Keep the Faith, my friends! We are the saviors of the Republic! Now and Forever!)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)
Contact the WWI Museum in Kansas City. It’s not a military uniform but it could be an auxiliary of some sort or a girls group to support the war effort. They have rearchers and volunteers who are experts and great archives. It’s the only museum dedicated to WWI in the country. They just did a major overhaul and expansion. If you’re in the area its really worth visiting. But you could probably email the picture and question. Go to their website.
Have u tried making your inquiry on ancestry.com?
If your timeline is accurate and she was 14 in that photo then that would put it at around 1919 right in the middle of the Spanish Flu Pandemic. There was a critical shortage of nurses and volunteers to give aid to the sick and she may have been involved somehow. I couldn’t find any uniform photo’s
One more suggestion you can go to the Smithsonian On-line and ask a librarian. There is a link for that.
It’s a middy blouse, very popular in the late 19th century up until the 1920s.