Yes. The sentence with correct parallel structure would be as follows. The doctor known only that her patient would improve, but also knew that her patient would [can't understand the sentence after that, but nevertheless it is still faulty].
The answer is yes. However, the other respondent provided you with an inaccurate (and non-parallel) sentence correction. The correct syntax -- and parallel structure -- is... The doctor not only knew that her patient would improve, but she also knew that he would completely recover.
The Importance of Being Earnest" is actually a comedy play that was written by Oscar Wilde and based on the excerpt taken from this in Act II, the two meanings of the word little that the pun in this excerpt relies on are SMALL and YOUNG. Hope this answer helps.
