There’s only a very short time I believe that it’s too early to begin playing with your kids. When’s the first time you picked them up and had them pretend they were an airplane while you swung them around?
I know, not quite a roleplaying game. However, very early on you build the foundation of playing games with your child, and there’s absolutely no reason ‘Let’s pretend’ can’t be a huge part of that. At 3-4 when your kids are pretending to shoot bows and arrows, play with him/her. Dice aren’t even neccessary. At that point, you’re roleplaying. Your child the bit of an archer, and you of whatever else. Maybe you’re both pretending to shoot deer as my nephew and his father did.
Move on from there as they’re ready. You can introduce settings, creatures, let them play out and pretend they’re in their favorite Disney movies or the like. Can introduce the concept of not -always- succeeding, show them how in the movies that it’s more exciting when the hero isn’t perfect. Sure he always wins, but, there’s usually a hold up. If he rescue’d the princess right off, there wouldn’t be much entertaining about it would there? Aladdin never would have met the genie if he could have just hooked up with the princess, for example. Still don’t need dice, or character sheets, at this point in time, use a coin, or play rock paper scissors.
When they’re ready, you can start introducing the concept of statistics, when you pretend you’re ‘blah’, he’s -really- strong, right? So, when he tries to do things that require alot of strength, he has an easier time, right? …
I could probably babble on the better half of a novel, but, I think the point is well on the way to leading to many more possibilities. Hope this helps!