First of all, there's actually such a thing as a Civil War Nurse Barbie. (But no Civil War Soldier Ken, featuring horrific battle injuries).
Second, it's been pointed out in a number of places (such as here and here) that the doll is historically inaccurate. So it teaches kids bad history.
Dorothea Dix, Superintendent of Female nurses, famously set strict guidelines for all Union nurses: "They were required to be between 35-50 years old and plain-looking. [No attractive young nurses!] They were to dress in black or brown dresses and were not allowed to wear jewelry of any kind."
This is what an actual Civil War nurses' uniform looked like, complete with bloodstains:
Unlike the Union, the Confederates didn't have a nurses organization that defined what nurses should wear. But Confederate nurses tended to dress in simple, plain dresses, because that was practical.