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.
My mother said she did sewing in the WPA, but I can’t find any pics anywhere that show that WPA workers had ‘uniforms’. If the style was popular back then, I suppose it could be a hand-me-down or charity because I believe they were very poor.
I agree. She’s too young to be a CPO. According to the OP, this was 1918-1920, so its probably just a fashion that looks like a military uniform. She wouldn’t have been a Sea Scout, if they even existed then.