I could be wrong, but I don't remember McCarthy ever telling the reader the age of the boy. As an author, he tends to let the reader make up ther own mind about a lot of things/leaves a lot unsaid or unspecified. This is very true in No Country for Old Men too.
I got the impression the boy was quite young, as his mother was pregnant with him at the time of the disaster that made the world so unliveable. It seemed he was about eight years old, perhaps ten, in that he can speak well, doesn't need to be carried, but is still small and unable to fend for himself like a teenage might be able to.