We were blessed with our twin sons in March of 2000 and my wife knew that they would eventually game, she even at a garage sale saw some 1st ed books and made sure to buy them so the kids would each have there own phb's.
Anyhoo, we started by looking at figures and dice, and of course many stories when they would be going to bed. Finally at 4 they wanted to play after watching mommy play. We made it easy and it went really well, we continued and now have a small campaign going with them as the focus. It is obviously rule lite, and they enjoy it, we let them decide if they want to play and then it becomes a reward for the day.
Huge fun, they like seeing the new monsters and figuring out what must be done, now we are trying to find good pictures of treasure and they want to find the "hidden" treasure guarded by the monster.
Their brother just turned two and he really likes the dice now, really big ones that he can't swallow are what we give him, he is really good at throwing them.
Finally...CONGRATS you have started a journey that will have no end...and you will find that your protective instincts over other kids also has gotten a lot larger!