Is marrying a girl without her parents' knowledge considered a legitimate marriage, and is proceeding with this marriage an act of disobedience and disrespect toward parents who object to my marrying her?

You are not permitted to marry a woman without a wali (legal guardian), for marriage without a wali is invalid according to the majority of scholars. A woman may refer her case to a judge if her wali prevents her from marrying an eligible suitor without a valid reason.

If your parents prevent you from marrying a woman for a legitimate religious reason, then you are obliged to obey them. However, if their prevention is without a valid reason, you are not bound to obey them, nor would you be considered disobedient to them. Nevertheless, it is preferable to obey them and seek another woman whom your parents approve of, as long as you do not suffer harm by forsaking marriage to the one you desire. If you do not have a compelling need to marry, then there is no necessity for it, and live with your wife in kindness.