I'm certainly no Sarah Palin (insert many, many jokes at my expense here), but for what's it worth, here's my take on the "Bush Doctrine" from February of 2003:
By focusing so much attention on the Iraq and Al Qaeda connection I think people are missing the bigger picture. This war on terrorism isn't just about Al Qaeda and it isn't just about Iraq and it isn't just about eliminating the threat that they both pose. After 9/11 Bush could have come out and said, "We have been attacked by Al Qaeda and will now wage war against them until they are wiped out."
But he didn't limit the war or the war's objectives to the destruction of Al Qaeda. He chose instead to embark on a wide ranging and long run course of action whose ultimate goal is a sweeping historical change of the world's political landscape. Terrorists and the countries that support them were served notice that they will no longer be able to carry on as they have for the last thirty years. The terrorists will be hunted down and eliminated and the countries they fund, support, and harbor will cease doing so or have their regimes toppled.
In some cases this will be the result of direct military action, in others through the use of economic and diplomatic levers, and finally in others through internal revolts. This program might seem impossibly grandiose and over reaching to some but I believe that this is what Bush has in mind. He got into trouble when he labeled it a "crusade" shortly after 9/11 but in many ways that is an apt description of it.
The Bush Doctrine if you would call it that seeks a world where nations are free to develop economically and politically without fear of terrorism or rogue regimes brandishing weapons of mass destruction. It is a remarkably ambitious and some would say unrealistic goal but I believe that the rewards of peace and stability are worth the sacrifices and costs that must be paid to achieve them. I don't know if most Americans would agree with my sentiments or if they really understand the nature of the war that we're now involved in but if you want to understand Bush's attitude towards Iraq you need to put it in the context of his larger perspective of the war on terror. It's much bigger than just Saddam and Osama.
This is just one deservedly obscure blogger's take, but I think it shows that when you say "Bush Doctrine" there is no easy, cut and dried defintion of exactly what the term means and to criticize Palin for not coming up with an answer that mirrors what Gibson interprets it to mean is not reasonable.