From what I gathered, she thought she could get away with it, because he was the weakest of the Old Gods. I bet Xal'atath told her, when she was with the Naga after the Sundering ^^ She didn't want to serve the weakest of them.
This is the broadcast text in the raid (the first few lines are the Inquisitor, I think):
Submit, Azshara! Beg forgiveness for your failure! Your betrayal!
Insolence only prolongs your agony! You will break, or I will carve out your defiant tongue!
Impudent underling! You will... address me... as queen!
More likely, Xanesh... Azeroth's champions... will be the ones... to silence you.
Release me! Only I possess the means of defeating N'Zoth!
Mind your tone, whelpling. A queen keeps her promises. Listen closely, as I will only say this once.
For all his bluster, N'Zoth was ever the weakest of his kin. One vestige of their power yet remains that can be turned against him.
I would have driven this blade into his foul heart myself... had you not disrupted my plans.
No matter. Xal'atath is yours, mortals. Strike true. Should your first blow fail, you will not survive to attempt another.
Edit: Seeing as N'Zoth knows this, because he is punishing her for her deal with Sylvanas and knows full well that Azshara got the dagger back, I can't see how he hasn't planned for this and maybe even relies on being "killed" by the dagger.