I've seen many little ones (even infants) ride Pirates with no issues. There aren't a lot of super-loud noises and the dark may even be calming if you're keeping them close...so I second this one!
As soon as I saw the title, I was going to say the same thing. It's a Small World. Definitely. Hold off on Winnie the Pooh until you have a few dark rides under your belt. Some kids find it scary. Back in 2009, my 4.5 year old was TERRIFIED of dark rides after Pooh and she didn't want to ride another one for the next 2 days. Same for UTS. My kids were all fine on UTS in May, but some kids COULD be afraid.
It's good to have a ride like IASW under your belt because if the baby gets scared, you can then go on IASW again to remind him or her that dark rides are not scary. Also in Epcot, the Mexico ride can serve the same purpose.
Other good picks are Dumbo, the Carousel, or the Magic Carpets. As for dark rides, after IASW, Peter Pan is a good pick. It's not scary at all.
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