The proper small-government response to 9/11 would be to send a punitive military expedition to the Middle East. Find the enemy, kill them, and leave smoking ruins.
But don’t tell them how to live, or what kind of government they should have.
But don't forget that immediately after 9/11, the Lugnut Rockwell types opposed doing exactly that. They used all the same arguments against intervention of any kind, even only in Afghanistan, that they now use against Iraq.
Problem is that a “private military” must be maintained at high (and expensive) tempo in peace time to achieve those kind of capabilities. And indiscriminate killing in today’s wired world creates more enemies than it kills.
BTW, how “private” can an organization be when it only has one client and all its operating parameters are tightly set by the government?