To be honest, the problem with Iraq is not Islam as such. The European powers that had divided up the world into their empires were very cleaver. When they finally had to abandon their game, they set up artificial borders everywhere that mixed conflicting groups. This assured that they would not rise to power and challenge their old oppressors.
'Iraq' had never existed as a country in its present configuration. The same is true throughout the Middle East, Africa and parts of the rest of the world.
Thinking that democracy can just be imported like Campbell's soup is the height of absurdity. It is a fragile thing and works, if at all, only in stable countries over a period of time.
Islam is not necessarily anti-democratic, though arguably it does lend to authoritarianism. But, remember, even with religion Iraq is divided into violently opposed sects. Ireland had 'troubles', too, and it wasn't Islamic.
