Does Oedipus have the courage to face his downfall? Although he accepts his fate, but doesnt plucking out his eyes means his lack of courage to face up the truths?
Oedipus does accept his fate, and we don't necessarily have to read his act of self-blinding as a sign of his unwillingness to face up to truth. Throughout the play, Oedipus had many opportunities to stop seeking the truth, and even once he began to understand some of the awful truth, he continued to press on so that he would know all. It is for the good of the kingdom, after all, which suffers cruelly as a result of Laius's unsolved and unpunished murder.
All this time, however, Oedipus has been figuratively blind: unable to see how his own pride and anger could lead to his downfall. Compare him to Teiresias, a prophet who cannot literally see but who can figuratively see; Oedipus was the reverse -- he possessed physical sight but lacked insight. When he plucks out his eyes, he renders his physical self as blind as his metaphysical self, and it almost feels like an act of penance. He blindly and arrogantly thought that he could outwit the gods and avoid their oracle's prophecy, and now this is part of how he pays for it.
In the final lines, Creon tells Oedipus to stop giving orders and expecting to have everything his way. Oedipus is, finally, led away by Creon and helped by his daughters. The fact that he allows Creon to have the last word and is led silently from the scene is one reason to believe that he has, indeed, accepted his fate and moves forward with (figurative) eyes wide open.
In some ways, one can say that Oedipus in Sophocles’ Oedipus Rex is extremely courageous in his unrelenting pursuit of the truth, and that facing his fate is a matter of unmasking a very unpleasant truth. On the other hand, he left Corinth in order to avoid the fate predicted by the oracle. So until the end of the play, when Oedipus blinds himself, one can say that Oedipus was blind to the impossibility of escaping the will of the gods. It is only once Oedipus has accepted his really awful fate of killing his father and marrying his mother and blinded himself that, in another play by Sophocles, Oedipus at Colonus, he finds out that, in fact, he has another fate (a good one) in store for him.