[Lockspur]

I'm thinking a pocket pistol would be more feasible for an accidental discharge. It's concealed from the public, but the shooter would still have purchase of it given the overcoats of the time. That being said, you're probably looking at a .36 cal ball round.

A torso wound would not end well. But if that round has to travel through an overcoat (the shooter) and then possibly the overcoat/petticoat then corset of the victim, I would say cavitation might be non-lethal. The bullet's deformation as it travels through cloth barriers would cause it to tumble with an unpredictable trajectory. Now. Weather conditions. Is it raining? An umbrella could be a convenient barrier (rods or support pieces taking the hit) that might be a pivot point for the readers' belief in the severity of the wound. Heck, an iron eyelet of her corset would make a decent impact point. Taking some of the silk lace with it into her wound...making it easier for extraction later.

As for organs. Why not kidney? We've got two. One can go and no one would be any the wiser. You might have to address whether sepsis is a factor in her prognosis, however.