To what extent does Desdemona's behaviour lead to her tragic end in Othello?
Short answer: To the extent that Desdemona becomes submissive and allows herself to be victimized, as well as her lying about the loss of the treasured handkerchief that Othello gives her, she contributes to her tragic end.
It is so often one of the great ironies of marriages that what first attracts people to one another and leads to their engagement and wedding often becomes the same element that effects the undoing of those marriages. Desdemona's attraction to the great warrior who tells her exciting tales of battle excites her to a desire to be part of his life. He, in turn, may well be attracted by her fierce independence in her conviction to marry him against the social prejudices of her Venetian society, as well as her allegiance to him when she speaks to her father who demands her obedience:
I am hitherto your daughter. But here’s my husband.And so much duty as my mother showedTo you, preferring you before her father,So much I challenge that I may professDue to the Moor my lord. (1.3.186-190)
EMILIA. Here's a change, indeed,
DESDEMONA. 'Tis meet I should be used so, very meet.
How have I been behaved that he might stick.
The small'st opinion on my least misuse. (4.2.111-114)