Hello,
Logically that makes no sense, if they had no knowledge of the law until they fell, then they couldn't have sinned, as the law is the knowledge of sin. That one command not to eat the fruit is not considered "the law" that identifies sin, that was one separate command which God specifically spoke to Adam and Eve as a test, a bit like God commanding Abraham to sacrifice Isaac, that was not "the law" which identifies sin, that does not encompass the "law" it was also a test. When Adam and Eve disobeyed God's command, they also broke the 10 Commandments and hence sinned.
Where does it say that they only received the "full knowledge of the law" after they fell?, All Adam and Eve received was a knowledge of "good and evil", sin and it's consequences, they had not known the concept of "evil" before committing sin, and yet they had known good. God's law is good, in fact the "perfect law of liberty". Even without sin, one can have a full knowledge of the law.
I believe the "age of accountability" concept is laid out in scripture, although I am unaware of a specific age when one reaches the "age of accountability" and tend to agree with Evergreen that each person matures differently, God knows the hearts and minds of each.
God calls babies innocents, (Jer 2:34, 19:4), we all know that even babies can be naughty or "play up" to a degree, however, God still calls them "innocents" when do they become sinners then if there is no "age of accountablity"?
God Bless,
Harlin