It’s a little disheartening to see The Guardian of all sources using "sharia" as a scare-word. You can read a concise summary of what the word has meant to Muslims spiritually and politically in Khaled Abou El Fadl’s "Islam & the State: a Short History", beginning on p.17 of the pdf document. Actually the whole document is well worth reading at this time, containing a summary of what kinds of provisions and structures are needed in a democratic constitution of a Muslim state which also acknowledges Islamic tradition to preserve democratic institutions against theocracy. (It is a Rand document resulting from a conference of on the topic of the Afghan Constitution, held in 2003). I’m sorry it’s a pdf file instead of something more readable, but I did find an interesting summary of some of the various positions taken by pro-democracy reformers and Islamic legal scholars here while looking for a better version.
No one will be more upset than I to find the Taliban* version (and it is only one version, not the universal implied in the article)** of sharia arising in the new Iraqi Constitution. However, having read the only part of the leaked draft I’ve been able to find translated online here (it’s the draft bill of rights only), I think Owen is way overinterpreting the data. (I also wonder how she arrived at the notion that there was such a thing as "women’s rights" in a country where there was no such thing as human rights, period, but that’s another issue). A basic commitment to international human rights standards are explicitly articulated in the document, a lot depends on whether Islamic law is named as "a" or "the" main source of legislation (since I can’t find the phrase at all in the online document and I don’t trust journalists to understand the importance of this, I don’t feel that it’s possible to tell which way it is in the constitution at this point), and ultimately the most important issue is how the legislature and the judiciary are structured with respect to articulations about sharia and its enforcement (see the Rand document for more details on that).
I'd like to a translation of the rest of the constitution; I won’t have much of an idea what to think about it until I do.
*Not to mention surprised; Iran is a much likelier model for the worst-case scenario in Iraq.
**It is, btw, grotesque to imply as Owen does that honor killing is enjoined by any traditional version of Islamic law; it is not and never has been. Although some Muslim countries, for example secular woman-friendly Iraq in 1999, have decriminalized it.