Let me begin by stating there is no such age mentioned in the Bible. Most believe that the "age" varies from child to child. While one child may understand he must answer to God for his sin at the age of three, another child may become aware at the age of eight. Mentally handicapped individuals may never become aware, and like newborns, would not be held accountable.
There are two kinds of sins, both requiring knowledge of God's will: sins of commission, which involve breaking God's Law (1 Jn. 3:4), and sins of omission (Jam. 4:17). In other words, for one to sin, one needs to be aware that he is answerable to God for purposely defying Him, and then to do so.
As for the belief that a newborn is a sinner because he has inherited a sin nature from Adam, Ezekiel 18:20 would challenge that. It says, "The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him." If a newborn does not bear the iniquity of his own father, how can he bear the iniquity of Adam? As I pointed out on May 6, we are "in Adam" because we sin (Rom. 5:12).
The consequences of Adam's sin (Gen. 3:17-19) clearly plague humanity to this day, but those consequences effect the physical world, and not the spiritual. Let's say your father is an alcoholic, and he wrecks his car with you in it. Your physical injuries are the result of his sin, but that does not make you an alcoholic, nor does it make you guilty of drunken driving. However, when you are old enough to legally drive and old enough to legally drink, should you choose to do both, you are guilty. Of course, in such a case, even if you were under age, say twelve, should you do those things, you are still guilty. The key here is that the individual has knowledge of the law, and chooses to break it. A two year old, having found his fathers alcohol, and left in a running car, would not be guilty if he pulls the gear shift into drive.
The bible shouts loudly from its pages that we are all free-will agents, and each one of us will have to give an account for what we do -- not for the sins of others. We all suffer the physical consequences of both our own sins and the sins of others. However, we fall victims to the spiritual consequences of other people's sins only when we follow them into sin ourselves.
You can't have it both ways;
either there is original sin,
or there is an age at which one is accountable.