Check out Aviation Week and Space Technology (September 1, 2003). There is a article in there on page 46 about reopening the Baghdad airport. This is basically what it said...
It says basically reopening the airport is a big goal for the Coalition Provisional Authority (CPA) since its important for revitalising the economy as well as a sign of stability. However its going to be hard for several reasons, mostly because of the guerrilla attacks in the area, as well as as soon as the airport was reopened, it would be a obvious target because the rail line was attacked the day that train service was restored to Jordan, and the oil pipline was attacked within 3 days of reopening, so undoubtably the civil airplanes would be a target, sucessful or not. So therefore, no airline wants to be first to fly in to Baghdad.
Another huge problem for the airport is the lack of infrastructure, which has been more or less destroyed over the past 12 years, as well as the aircraft there have been stripped of parts and looted.
Right now the CPA plans to open up Baghdad (which would have 3 flights daily when initially opened), Mosul, and Basra which will cost approx. $91 Million.
There are a lot of airlines trying to get in to the airports as soon as it opens though. 30 airlines applied to Baghdad, and 16 for Basra. Right now, it looks like Brasa will open first, because its more stable as far as attacks are concerned, and 6 airlines currently have permission to fly into Basra when it opens in a few weeks, SAS, LOT, Qatar Airways, Gulf Air, Royal Jordanian, and Emirates. British Airways was also granted permission, but has not set a date.
As far as Iraqi Airways, 2 of 23 airplanes were destroyed in fighting, 8 were looted and stripped of engines (however most were found), there are 15 airplanes scattered in Tunisia, Jordan, Kuwait, and Iran, which have been there since 1991. Apparently lots of contractors have contacted the CPA to start up a new national airline, or restore Iraqi Airways, but it looks grim due to "huge debt and a 'demolished' infrastructure" so it may be a while, it was also mentioned it would take at least two years to get a new airline up and running.
Hope that answered some questions.