The vast majority of rides at WDW have no height requirement. This includes all the rides in the Magic Kingdom's Fantasyland, such as Peter Pan, Small World, Dumbo, etc. You can take a baby, toddler, or preschooler with you on any of these rides.
However, for safety reasons, there are some attractions that do require guests to be of a certain height to participate. The exact height required varies depending on the attraction. Some rides require that guests be only 35" tall, while others require that they be 52" tall, as well as various points in between.
If you look at this page of travel tips for people with small children found
HERE,
you will see a button on the right hand side of the page that says
"Height Requirements." Clicking on this link will bring you to handy
pdf that you can download. The pdf lists the attractions in all four
theme parks and both water parks that have height requirements. If an
attraction is not listed on this document it means that there is no
height requirement and any age child can enjoy the ride.
The height requirements are also listed on all the maps at the parks and on signage in front of the various attractions.
Have a great vacation with your family!