We took our 11-month-old twins to Cayman for 10 days and had a ball. Now we're considering Disneyworld this fall, when they'll be about one and a half.
We've also taken them on extensive travels throughout Ontario and to Vermont. They love airplanes and boats as well as cars. Ours have been travelling since they were just weeks old. So we so no problem travelling with three year olds.
Having said that, which I did to respond to some of the negativity here, the OP's question wasn't WHETHER to travel to Disney but to WHICH Disney. While we haven't made it to Disney yet with the twins, we have done a fair bit of research and have concluded our first choice is Disney World in Florida.
Our rationale includes the onsite accommodation choices, the ease of transportation to the various attractions with children, the ability to return to our hotel room at any time, and the vast array of attractions - which are just as much of interest to us as well as they are to the kids. While our dynamic duo might not know Mickey from Goofy, they sure know fun when they see it! And they love the water, which abounds at DW.
That's our view, anyway.
Cheers,
PS - At the risk of being provocative, I can't resist adding w've already booked our flights to Australia in January to take advantage of flying free before the kids turn two!