To what extent are issues of gender central to the tragedy of Othello?This is the question for my coursework essay due very, very soon. At first we...

It's difficult to help you without knowing your plan for
writing (I don't want to confuse you more!), so I'll just present some important issues
for you to consider.  (I'm assuming that you're already examining the relationship
between Desdemona and Othello.)  Here are some other things to
consider:

It's interesting to look at Emilia's relationship
with Iago.  Specifically, Emilia's willingness to take Desdemona's handkerchief (and to
look on as Othello reprimands Desdemona for losing it) certainly suggests some level of
subservience ("I nothing but to please his fantasy" (3.3.343).)  In Act 5, though,
Emilia repeats that though it is generally "proper" that she obey her husband, she will
not do so at that time--and insists that she will "ne'er go home."  Emilia has
recognized that damage both she and her husband have done, but since Desdemona is
already dead, she speaks against her husband too late.

Also
of interest is the conversation between Desdemona and Emilia in Act 4, scene 3.  As the
two discuss marital infidelity, Desdemona insists that she can't imagine that any women
would be unfaithful to their husbands.  Emilia, on the other hand, argues that women
have the same desires that men have--and blames husbands for their wives' infidelity. 
Here, Emilia seems to have a more progressive (and some would argue realistic) view on
relationships.

Finally, it's important to look at
Desdemona's willingness to stand up to Iago in Act 2, when he openly makes fun of his
wife (and women in general).  Emilia, though she is outspoken and defies her husband
later in the play, is relatively silent.  Desdemona also openly (and confidently)
defends her marriage to Othello, telling her father, and the Duke and Senators, that she
chose him as her husband and will be loyal to him.  While these passages reveal
Desdemona as a strong woman, she is often criticized for not defending herself enough
when she observes a change in Othello's behavior. 

(If you
choose, you can also examine Bianca's role in the play; look at Cassio's relationship
with her and Iago's willingness to blame her for Cassio's attack in Act
5.)

Good luck!