I'm actually surprised that she accepted your dinner invitation, as it would seem a little unprofessional to go to a patients house for dinner, but perhaps after dealing with her for so long she feels comfortable enough to do this. It's not abnormal for someone who has gone through as much as you have, and to have put so much trust in your doctor, to develop feelings for them, they are after all in many ways responsible for our health and wellness. We look at them much the way we look at priests, or lawyers, they have the inside line on how to make it right and they hold so much power in their hands, so it's natural to look up to them.
I would hold off on expressing your feelings just yet. Let her come to dinner and you can spend some quality time with her as a friend. It would not only be unethical, but illegal for the two of you to become involved romantically, but if that's the way that this is going, then you would have to find out the time frame within which you would have to dismiss her as your doctor before you could become involved.
It's not 'wrong' to feel any particular way about someone, it's only wrong if it hurts other people, so it's important to know the right thing to do under any circumstance.
I welcome your thoughts, let me know if you want to talk more