Wrong. Iraq was listed as a state sponsor of terrorism by the State Department for more than a decade prior to 9/11. The Bush Doctrine was formulated after 9/11. It stated that we would go after the terrorists and the states that supported them.
It would have been foolish to allow Saddam to stay in power and provide sanctuary and resources in support of AQ, including WMD. Prior to 9/11, as the 9/11 Commission documented, there were contacts between Iraq's intelligence service and AQ. There were also 17 UN resolutions against Iraq and its failure to comply with the truce agreement ending the first Gulf War.
It is also worth noting that the US and the UK had been bombing Iraq daily for almost ten years to enforce the Northern and Southern no-fly zones. Leaving Saddam around while fighting the War on Terrorism was not an acceptable option.
Bush's advisors are neo-cons. His doctrine is the neo-con doctrine. Irag as a base from which we can project power was always a keystone of that doctrine.