No Meteorite
It is one of the myths floating around the Internet that Ayers rock is:
a) Unlike any other nearby rock
and
b) A meteorite that has fallen from space
Both are false. A few tens of km away, more of the same rock outcrops in the mountain range called the Olgas, as seen in the picture below. Ayers Rock (Uluru) is the blob on the right, the Olgas the lumpy patch on the left. 
and a meteorite origin is ruled out because Ayers rock is a stack of sedimentary sandstones, has no impact crater around it, and is undamaged by the alleged fall.
The only geologically odd thing about Ayers rock is that the bedding is vertical, due to fold movements in the past.