Desdemona is clear that she will be loyal to her husband as soon as their marriage is public. She explains her ‘divided duty’ as a daughter and a wife, but as tradition dictates, her allegiance will pass to her husband-
I am hitherto your daughter. But here's my husband,
And so much duty as my mother show'd
To you, preferring you before her father,
So much I challenge that I may profess
Due to the Moor, my lord.
When discussing with Emilia their relationships with their respective husbands, Desdemona is adamant that she would remain loyal to her husband, and would not betray him
for the whole world.
It is Desdemona’s final words which clearly assert her loyalty to Othello. Despite being told she is on her death bed, Desdemona refuses to confess to a liaison with Cassio which did not happen-
I never did
Offend you in my life; never loved Cassio
But with such general warranty of heaven
As I might love.
Her final act of loyalty to her husband is to condemn her self to purgatory as she lies on her death bed to protect Othello. She refuses to identify him as her murderer and blames herself for her own death-
O, who hath done this deed?
Nobody; I myself. Farewell;
Commend me to my kind lord. O, farewell!