Basis for the concept of an "Age of accountability"

Having attended Baptist Churches for years, I've often heard the term "age of accountability" bandied about. The idea is that if a child dies at a young age - before reaching the "age of accountability", that child will go to Heaven, because he or she is not yet responsible for his or her sins. He or she is "too young to understand the Gospel". This age is not a specific age, but is understood to be different for everyone. I'm ***not*** asking what this age is. ***What I am asking, is where is the Scriptural evidence to support such a doctrine?*** Quite frankly, one of the reasons I stick to Baptist Churches is not because I consider myself a Baptist, but because it's the one denomination where in my (admittedly limited) experience, Pastors consistently say "If I ever preach anything that's not in the Word, or contrary to the Word, don't believe me." Yet, I can find no Scriptural evidence for such a doctrine. Am I missing it? If so, where is it in Scripture? If it exists, please point me to the verses. Or is it a doctrine based on supposition, attempting to reconcile the idea that a loving God, and the horrific idea that child could go to Hell simply for not being old enough to understand their lost state, repent, and put their faith in Christ?