There Was No Al Qaeda In Iraq Before 2003

I don't know how many times I have heard people say that there was no Al Qaeda in Iraq before 2003.  It is a true statement, but do people who make this statement ask why?  Why did Al Qaeda, the Base of God's Support, not attack Saddam Hussein's secular regime, who murdered countless Iraqi Muslims for wanting an Islamic government in Iraq?  Did Saddam possess some kind of mojo (doubtful) that kept Al Qaeda suicide bombers out of Iraq?  It seems that when people say that there was no Al Qaeda in Iraq before 2003, they are giving kudos to Saddam and his henchmen, as if to say they were doing something right.  Did the regime build a wall along the Iraqi-Saudi border that we don't know about?  How did Saddam keep Al Qaeda out of Iraq?  Did Al Qaeda even think of destabilizing Iraq before 2003 by suicide bombers, car bombs, and attacking government officials? 

If Al Qaeda is concerned only with attacking Arab governments that cooperate with foreign occupiers, why hasn't Al Qaeda ever attacked government officials in Qatar, the Arab Muslim country that hosts the United States Central Command ( CENTCOM)?  Has a suicide bomber ever blown himself up among people in Doha?  We don't we see Al Qaeda attacking the forces of Mahmud Abbas, who has cooperated with Israeli occupiers for many years now?