The Puritans didn't think four was too young an age to begin learning the basic tenets of the Christian faith. Many of their children began memorizing the Westminster Catechism at no later than five, and some started as early as age three. It's not that all their children were geniuses; it's just that they took the spiritual discipline and instruction of their offspring very, very seriously.
Most of us assume really young kids aren't capable of understanding theology and doctrine, and in some ways they aren't, but whether they get it all right away or not isn't the point. The point is that God instructs us to raise our children in His name, and that they're never too young to hear the truths of His character described and expounded.
Spiritual understanding isn't the same as intellectual knowledge, anyway. While it takes hard mental work to do calculus or write a research paper, God's truth comes to us largely through His Spirit. That's not to say we just let the Holy Spirit guide us; we need the wisdom of godly men and the exercise of logic to understand the Bible, but anything we understand about God is through Him and not our own efforts.
How are we, therefore, to say what our kids do or do not understand? Our duty as Christian parents isn't to determine what the young ones will "get" and only teach those things; it's to instruct them in the whole of God's truth, and show them the way of righteousness both through God's Word and the example of other Christians (including ourselves!).
We think it's a good idea to start with the story of the Bible, but there are a couple things we don't mean by that. One, individual stories shouldn't be plucked out of context and turned into little morality tales; the whole story of Scripture needs to be explored, with a constant focus on Christ as the central and unifying theme. Second, the Bible narrative is full of doctrine and theological insight, and should be read and studied with that in mind.
In our postmodern culture, there's a lot of noise being made about the redemptive nature and power of stories. We don't disagree—but stories are only redemptive if they impart truth, particularly God's truth. The story contained in God's Word, of man's Fall and Christ's redemptive work, is the only one that perfectly reveals God's Truth, and therefore the only perfectly redemptive story.
There's also more to it than just characters, plot, and action. Each part of the story tells us something about God's character and nature, guiding us to deeper faith, deeper love, and more obedient living. These are the things we want and ought to show our kids, the most important elements of any Christian education, and no child is too young to start learning them.