Answer: She does not want to fall in love with anyone.
The phrase "to be hit with Cupid's arrow" is based on classical mythology. Cupid is the son of Venus and Mars and he is associated with love and desire. He carries arrows with which he shoots his victims. When a person is hit by an arrow from Cupid, he falls in love. Therefore, as the quote states that she will not be hit with an arrow, the implication is that she will not fall in love with anyone.