[Aristoddler]

If god had doubts about himself, would he be an agnostic?

Nope.
And he could make a rock big enough, sure...but where would he put it?
It would have to be bigger than creation, and that would require him to make something bigger than that which he had already created...which is existence.

Therefore you would first have to determine how big existence is, before determining the size of the rock, and then you would no doubt come to the conclusion that god has limits.
Once you come to that conclusion, then you would prove that god is in actuality...fallible.
I believe that at that point the cosmos would cease to exist, so please stop thinking about it before you destroy us all.