Couple of suggestions…
First, check out the forums at Fear the Boot. (Their default color setting is awful, but if you register you can change the skin, so don’t let that set you back.) ANYWAY, that forum is by, for, and about people who want to game and get others involved. These guys have a LOT of great suggestions, and most will be very helpful to you with suggestions and ideas.
Second: their first suggestion for getting people interested in gaming is to try “Settlers of Catan”. I haven’t played it yet, although I’ve been told I’m going to get the opportunity soon, so I haven’t the foggiest whether or not it’s good for kids. 21 months is a little young yet, but it’d be a good board game / “gateway game” for the FAMILY to play at, say, Thanksgiving. And hey, if you can get mom & dad interested in RPGs through “Settlers”, then maybe the kid will be interested too, later on, without you having to put forth a HUGE effort, hey?
Third: A great RPG for kids to play is “Toon”, by Steve Jackson Games. Toon is based on all the great cartoons you remember as a kid - it uses cartoon logic, and you can do dang near anything. We own all the books (oooohhh, except Toon Munchkin, now I know what DogDad’s getting for his birthday…) and the best way to play this one with kids is to explain the rules, give 'em an character (or hey, have 'em make their own if they want) and then run 'em through a few scenarios. We play a rather loosey-goosey game: if we’re having fun, the GM lets us go and have our adventure rather than “roll the dice to see if it worked…okay, now roll again to see what happens”. The GM is pretty much there to start the scenario going, provide the start, the end, and the “mission” and then lets us go. Oh, and to act out all the NPCs, of course.
The kids (and adults) we’ve played with love that, and it’s easy enough to design (or adapt) the prefab adventures they have for anywhere from an hour to an all-night adventure. Great for one-shots…and if you want to eventually get on to protracted campaigns, you can do those, too - it’s all up to you.