"A nineteenth century woman wouldn't have done that anymore than I would take my shirt off on a hot day."

Sorry - not true. There are several instances of women going so far as to enlist in both sides of that particular militant disagreement and serving at the front. A friend of mine, seriously into history for its own sake, found herself drawn into re-enacting. She researched a couple of these women and went so far as to portray them and act as a "historic interpreter."

One woman (I've forgotten her name and unit, although I believe she was with a New York regiment) enlisted and served for three years. She was "discovered" in a field hospital after being wounded... the third time.   

Regards -

Pete