Part of what makes William Shakespeare's Othello a tragedy is that once the main events of the plot are set in motion, there is no way for the characters to escape the unhappy ending. Desdemona is completely faithful to Othello, and has done nothing wrong. Even her efforts to reconcile Cassio to Othello are motivated by kindness and love of her husband. She and Othello are victims of a plot by Iago, the evil character in the play.
In a sense, by asking if Desdemona could have done anything to avoid being a victim of domestic violence, the question seems to blame the victim. Desdemona did nothing wrong, just as most women who are victims of domestic violence are just that: victims. If a man attacks a woman (assuming it is not in self defence) then the attacker is the one to blame.