The topic of "Character is destiny" seems to fit Shakespeare's Hamlet quite well, as seen in the character of Hamlet. There are not too many others we can look to as examples of good character, except perhaps Ophelia, and certainly Horatio (a minor character).
"Character" is described as:
3. moral or ethical quality...; 4. qualities of honesty, courage, or the like; integrityOphelia has character—even though she is telling her father how Hamlet acts with her, she is simply following his directions as a dutiful daughter. For Ophelia is also quite torn between her sense of duty and her feelings—to the point that she goes insane. Honor itself does not directly define her to her destiny.
Horatio is a man of good character. He is an honest supporter of Hamlet. He is a friend who looks for nothing in return, but offers his support as Hamlet faces repeated adversity. Though a minor character, we could argue that "character is destiny" for him. An honorable man, he is left to tell Hamlet's story. Hamlet, then, seems to be the only other man who has true character. He needs proof that Claudius killed Old Hamlet before he acts. Hamlet plans to use the play (The Murder of Ganzago) to reenact his father's murder and watch for the King's reaction:
I'll have grounds
More relative than this. The play's the thing
Wherein I'll catch the conscience of the King. (II.ii.598-600)
He faults his mother for practicing what the Elizabethan audiences saw as incest in marrying her brother-in-law.
She married. O, most wicked speed, to post
With such dexterity to incestuous sheets! (I.ii.160)
He finds it difficult to see people drinking and acting drunk so publicly when the King celebrates his wedding to Gertrude. He feels that although it is customary, other countries think Denmark is filled with drunks. Hamlet also is offended that the wedding date took place seemingly while the leftovers from Old Hamlet's funeral were heated up and served at the wedding—(which is nothing but exaggeration); it is simply a way for Hamlet to express how quickly the wedding followed the funeral.
Thrift, thrift, Horatio. The funeral baked meats
Did coldly furnish forth the marriage tables. (I.ii.185-186)
He is also a honest man who (before learning of his father's murder) shows how he feels without hesitating. His mother tells Hamlet to put off his mourning of his father. Death is a part of life, but he seems to be taking it rather hard. He says...
Seems, madam? Nay, it is. I know not seems.
'tis not alone my inky cloak, good mother,
Nor customary suits of solemn black...
No, nor the fruitful river in the eye,
Nor...all forms, modes, shapes of grief,
That can denote me truly. These indeed seem,
For they are actions that a man might play;
But I have that within which passeth show,
These but the trappings and the suits of woe. (I.ii.79-84)
Hamlet notes that he does not "seem" full of grief—he is full of grief. While others might wear sadness as a disguise, Hamlet's sadness over his father is quite real.
Hamlet is a man who is governed by a sense of what is right; what is suitable; was is honest; and, what is ethical. He is a man of integrity. His love for his father and his sense of honesty require that he discover whether Claudius' hand has had a part in Old Hamlet's death. His character is destiny for it leads to his fate—only avoidable if he were a man without character, and Hamlet could not be less that he is.