QF is a terrorist target because it is a symbol of Australia. Have you seen the security at any Australian embassy or high commission ? Putting the flag carrier into a part of the world where it was recently involved in fighting a war alongside the great Satan might not be a good idea. It would be better to use an airline from a country not involved.
I've found it interesting to compare the US/British/Australian embassies with those from small neutral countries. In the first case the premises is usually a fortress, in the second the facility is often in a normal office block with little more security than any other tenant.