And I would address her as Dr. Doe, just as I would refer to my brother-in-law as Dr. D when he finishes his PharmD program (in person I will probably just call him by his first name, lol). Your D sees patients, they are expecting to see her, so her position shouldn't be a source of mystery. But in an ER setting, as was my example, when someone is expecting to see a physician, it would be confusing to them if someone referred to themselves as Dr. X when they are an NP with a DNP. Don't get me wrong, I love advancing one's education, I am a fan of board certs, and I put them on my badge when they apply. I keep flirting with various terminal degrees (can't decide), but with ER patients, even if I had a doctoral degree, I would just introduce myself as Pixie.RN. Those patients have enough confusion as it is!
Congrats to your daughter, by the way. A good friend of mine did the same thing (PhD in clinical psychology) after she already had a PhD in English lit. Omg, the years of school!!