The issue is specifically what is an honor killing. It is my understanding, and I will be corrected if I am wrong, that an honor killing is done because the victom (and they are innocent of anything deserving death) has done something that makes the family (usually the father) look bad.
Judaism would not allow this in any way, shape, or form. Even though i am not Jewish, I can tell that the cases where a death penulty is called for, even in the harshest of the old codes, is not very common. The specific case pointed out is a very limited one indeed. First, she would need to be the daughter of a priest. Note that there are no Jewish priests at this time. Second, the dishonor done, according to the earlier parts of the passage, have to do with her father’s standing as a priest. In other words, the people will question his holiness if this happens. Third, she must be an actual prostitute. I may be missing something, but often in the OT, this means priestess of a pagan diety. Often, they are called temple prostitutes.
Besides, Jaudaism, as pointed out, has a written part and an oral part that works with it. If you are saying that Jews defy God because they do not participate in the barbaric, brutal, anti-woman act of honor killing, you do not understand what God wants of us.