If she were my employee and I lived in a state where I could fire someone for any reason (other than being a member of a protected class) then I would absolutely fire her. Besides being offensive and disrespectful, what she did shows a serious lack of judgement. I wouldn't want someone like that representing my company, whether the picture was taken and posted on a work trip or not.
I agree with a previous poster that the "Obviously..." comment was particularly bad. No, nothing about that picture would make it obvious that she meant no disrespect to people who served the country. Honestly I don't see how anyone could think the picture wasn't intended to be disrespectful.
Personally, I don't care if her life is ruined by it. Actions have consequences. If your actions are egregious enough, they can have very significant consequences for a long time afterward. I doubt that her life really will be ruined but if it is, well that's her own fault. I feel the same about the Westboro morons. If their lives are ruined because of their idiotic conduct, that's fine. You may have the right to express yourself the way you want to (for the most part, at least) but that doesn't mean you're going to be immune to any fallout from it. You might find that people don't want to employ you or even associate with you if they dislike your actions enough. That's one reason it's important to think things through before you do them, and especially before you post them on the Internet!