Dahlia Litwick defends the the notion of a "Living Constitution" (in the American context) and mentions the Iraqi Constitution.
Mickey Kaus focuses on the actual text of the new constitution: he notes that it calls Islam "a fundamental source" of law and thinks that the word "a" ought to be seen as more important than the word "fundamental." But nothing binds the interpreters to Kaus's textualism. They might adopt the notion of a "Living Constitution" or something like it.
Whether the Iraqi Constitution invokes Islam as its source of law or not, what is more important is what those who apply the Constitution have to say about it. They could import Islamic law whether it's mentioned in the Constitution or not, and they could interpret that Islamic law in a way that respects the rights of women or not. They could also oppress women without referring to Islam.
Glenn Reynolds has this:
Americans are unusually legalistic and unusually focused on constitutions. But plenty of constitutions have wonderful language on paper (the old Soviet constitution was great that way) and plenty of countries (Britain, for example) manage to get by without written constitutions at all. What matters more is political culture. If the Iraqi people want a free, prosperous country and are willing to work for it, they'll get that. If they don't, or aren't, then they won't.