[quote=LegendBegins]
Not quite. "I'm good," in the sense of morality is little used, and makes no sense in the given situation. "I'm doing well," in accordance to the fact that she isn't sick, nor in any kind of peril, is the grammatically correct road.
[/quote]

I'm well = I am well. Well is an adverb in most contexts, and therefore (in those contexts) you can only apply it to action verbs, not linking verbs. "Am" is a linking verb. However, "I'm doing well" is perfectly fine.