Desdemona is unconventional in loving a Moor. That she would shun the "curled darlings of her nation" and fall in love "with what she should fear to look upon" shocks her father. Her elopement with Othello shows that she has a mind of her own. But what is most impressive about Desdemona is how she handles her father's public accusations against Othello in front of the Duke. Desdemona quietly, but assertively claims that she has a "divided duty." She recognizes that she owes her father her life and her education, but that as her mother before her made Brabantio her major allegiance, so must she do to Othello. When forced to choose, she chooses her husband over her father. This set of priorities would have been very appealing to Elizabethan audiences. Desdemona recognizes her father's objections, but she is strong enough to reject them for the love of her husband. Desdemona, in Act 1, acts quite admirably and independently. She swears she loves Othello, not for his "visage" but for his mind. By all appearance, Desdemona is a mature, young lady, who knows what she wants and is willing to stand up for it.
I think that Desdemona is fairly unconventional in how clearly she decides to break with her family in recognition of her love for Othello. I don't think that there are many examples at the time and even now of a character who is so willing to commit freely to another at such great cost to herself. Desdemona sacrifices so much in terms of leaving the comfort of her family in order to remain with Othello. Upon doing this, she remains loyal to him. I think this is another element that makes her unconventional. She actually loves him and does care for him, taking to domesticity in quite a harmonious manner. Conventional wisdom would probably have Desdemona being more anxious once she leaves with Othello. Yet, she is different in how happy she is. This makes Othello's tragic condition of fear and insecurity even more difficult, especially in contrast to her unconventional happy manner.