Not only does she not know
is a little more formal, and perhaps slightly better, than
Not only doesn't she know
But I'm worried about how you would continue the sentence. Double negatives sound awkward, so we tend (in BrE at least) to avoid the not only - but also formula when the verb is negative.
If we find we HAVE embarked on such a formula we often don't bother finishing it 'properly': "Not only does she not know: she doesn't even care." This might not be grammatically perfect but it is colloquial. It would be better and simpler to say,
She neither knows nor (cares)
She doesn't know and she doesn't (care).
If, on the other hand, the stress in your example is on "she", then you need to rewrite it. There are several better ways to say, "Not only does she not know, but also he doesn't." "She doesn't know but neither does he." Or less emphatically, "Neither of them knows." (Or "know". It is much discussed!)