I could be wrong, but I believe the idea of "the age of accountability" does not state that infants are "innocent," only that God might see them as such as they do not have a full understanding of their actions. It is not (in my understanding) a doctrine which states that God owes them heaven or grace, but that God, in his mercy, grants both to them.
so any doctrine we have is made of mens desire not Gods word.
Only if we have no idea what God is like from His self-revelation, both specific and general. I do not believe this is the case. From what we know of God's nature, we can develop a doctrine. We do this all the time on things like abortion.
The Calvinist points out that if this were true, it would be impossible for the infant or the bushman in Africa or the imbecile to be saved because they cannot participate in their own salvation by making the decision to "accept" God's "offer" of grace.
This problem is solved, however, by acknowledging that God's mercy is not conditional on anything but His own good purpose. The playing field is leveled for all of us. Either God wrote our names in the Book of Life from before the foundation of the world, or He didn't. No amount of cajoling can change that reality.
Thus, just like you and I are saved by faith alone, an unmerited gift from God to his fallen creation, so, too, might the infant and imbecile and bushman be saved, if it is God's will.
Because "deserves got nothing to do with it." - William Muny, "Unforgiven."