Hi Elizabeth,
Thank you so much for visiting the Disney Parks Moms Panel with your question! We on the panel love helping guests to plan magical vacations.
I have great news for you. There are many attractions that your 1-year-old can experience! The little one will be able to ride on all of the rides that you mentioned: it's a small world, The Many Adventures of Winnie the Pooh, and Peter Pan's Flight. I remember when my daughter was an infant, and she would request to ride it's a small world over and over again by making the sign language sign for "more!" Check out this list of
height requirements for Walt Disney World attractions. This will let you know which attractions do not have a height requirement so that your little one can ride.
Since you mention that you have an older child as well, that child might want to experience some slightly more thrilling attractions. If you find that this is the case, check out
Disney Rider Switch service. Using this service, if you have more than one adult in your group, one adult can wait with the little one while another experiences an attraction with the older child. Then you can swap and the second adult can experience the attraction without going through the regular queue!
A final thought when traveling with a little one: do check out the
Baby Care Centers. These are located in every theme park and are a great place to feed, change, and just take a break with your little one.
I hope that these thoughts are helpful for you, Elizabeth! Please do let us know if you have any further questions.