What would be the effect of a terrorist attack on the Statue of Liberty?
Certainly it would not be as easy to rebuild as the twin towers, and the effects on Americans would be alot worse.
What do you think would happen in the aftermath?
The statue is much much smaller and closer to the ground than the twin towers. It is likely that the plane would miss, hit the ground before the statue, miss left or right, or overshoot.
It is significantly (as in, several orders of magnitude) easier to rebuild than the towers, the death toll would be much much lower.
But foremost, the symbolic value of destroying the statue of liberty is not going to make a point for Al Qaeda. In their twisted view, the WTC - seat of the companies bankrolling the American Imperialism (tm) - and the Pentagon as the military HQ were "legitimate targets" of a perceived enemy. The statue would be, at worst, the symbolic fig leaf of pretended good intentions by said enemy, or at best, just a bunch of tourists. Contrary to the "they hate our freedom" idiocy spread after that, the AQ terrorists were brainwashed to believe that they were carrying out legitimate military strike, with the according choice of targets. This was actually the difference between centralized planning of the pre-9/11 Al Qaeda and the chaotic random attacks on civilians (probably locally planned and controlled) that took place afterwards - after the AQ command chain was shattered in the first weeks of the Afghanistan invasion. For pre-9/11 AQ, the thousands of victims were collateral damage, for the attacks afterwards they were the actual goal.
What you or I think of their mass-murderous insanity doesn't matter here...