That is a question I would like very much to know the answer to, because if the answer is a clear no, then it provides a strong moral case to encourage the Iraqi government to have Rand's father and two brothers prosecuted for her murder.
I have admittedly not dug that deep, but this is what I have found thus far.
Since many Muslims reject the United Nations Declaration on Human Rights because a number of its provisions run counter to Islamic law, an Islamic version was promulgated in response: The Cairo Declaration on Human Rights in Islam.
I read through the declaration to see what it had to say that might be relevant to "honor" killings.
For me, the most pertinent section was Article 2. Paragraph (a) of Article 2 reads "Life is a God-given gift and the right to life is guaranteed to every human being. It is the duty of individuals, societies and states to safeguard this right against any violation, and it is prohibited to take away life except for a shari'ah prescribed reason." Paragraph (d) reads "Safety from bodily harm is a guaranteed right. It is the duty of the state to safeguard it, and it is prohibited to breach it without a Shari'ah-prescribed reason."
So, was Rand Abdel-Qader's murder permissible under "a shari'ah prescribed reason"?
In my quick Google search, I came across this article from the Kuwaiti Times, which quotes a "Qais Al-Ameri, a member of the United Iraqi Alliance, [who] argues that honor killings are permitted under sharia law. "Illicit sex is the most dangerous thing in a society, and there should be severe punishments against those who practice it," he said."
Note that Qais Al-Ameri specified illicit sex. Rand Abdel-Qader was a virgin and did not engage in any sexual activity with the British soldier with whom she was infatuated. Unless speaking in public with a man falls under the umbrella of illicit sex in Islam, I would have to say that Abdel-Qader Ali's murder of his daughter was not permissible under Sharia law.
Granted, no woman or man deserves to die for engaging in sexual activity, but if any of us want to make any headway in convincing the Iraqi government to bring Rand's father and brothers to justice, then you have to play ball by their rules. And if a convincing case can be made that Rand's murder was contrary to Islamic law, then that might provide an avenue for prodding the Iraqi government to do the right thing in this case.