First of all, you are confusing a constitution with laws. They are distinct entities, with the former guiding and informing the latter. Thus it is entirely possible for them to lay down some basic rights in the constitution, even some that are distinctly contrary to Koranic teaching, and also decree that the
laws be consistent with Islam. Obviously this places limits on what Islamic teaching can be come law.
Secondly, we did not fight a war so that we could create an exact clone of the U.S. We're not perpetuating anything in Iraq. At worst, we are allowing things to continue so that we can accept progress towards an ultimate goal. It's not unlike the founding of this country. Many people we against slavery but they understood that unifying the country was, at the time, more important.