The Iraq war had no good reason to be fought in the first place, it was based on unfounded accusations by the Bush administration basically seizing upon the 9/11 event (that I do believe they had a hand in wholeheartedly, just look at the Gulf of Tonkin, Operation Northwinds, and the Reichstag Fire) that Iraq had WMD'S (none were found) and that the Iraqi Gov't had connections to al-Qaeda (none were found). 9/11 was a scapegoat that sacrificed the lives of innocent people, on that date and beyond. If 9/11 had not happened then Bush would have had no good reason to launch an attack on a nation that, coincidentally, his father had a previous bitter rivalry with during the Gulf War in 1990-1991, which resulted in heavy American occupation of Saudi Arabia, which pissed off Osama bin-Laden, which prompted him to plan 9/11 throughout the 90s before following through with it in 2001 which the Bush admin could have
easily prevented, but instead chose to capitalize off of due to Bush's inauguration a mere 7 and a half months prior beginning to appear to be nothing more than a lame-duck president.
But yeah, it's just a coincidence that his approval rating skyrocketed from an all-time-low to an all-time-high directly after 9/11.