Shouldn’t she have answered “yes, brother” instead of “no”? I mean, shouldn’t she have said "yes, brother. I have settled my mind and I will not marry her.
What think you? We have been in this city fully three weeks. Have you yet settled in your mind whether you will marry this dark-faced lover of yours, this Prince Rabadash, or no?”
The lady shook her head. “No, brother,” she said, “not for all the jewels in Tashbaan.”
This type of thing is common. She is not answering if it’s settled in her mind. She is saying what her decision is. By answering what her decisions is, it’s understood that she has indeed settled it in her mind.
Also, in the original question, it’s implied that the asker would like to know her decision, if she’s made one. If she simply answered “yes” and didn’t say any more, it would still leave the implied question unanswered and become an awkward situation.
If she simply answered yes, without stating her decision, it might be seen as a “smartass” answer since the asker obviously wanted to know what her decision is.