Hi Gianluca:
I'm a parent of two boys, ages 5 and 3, who have been traveling to Walt Disney World since they were infants. In my opinion, three is a perfect age to bring your daughter to Walt Disney World. She will likely enjoy the experience, and you will always remember it , and can capture parts of the trip through pictures and video that you can keep and share for a lifetime or longer. I would love to share some of my family's must-dos for our Disney World vacations. Your family may have different tastes, but hopefully these recommendations will be a good start to planning your trip.
Among many other things: at the Magic Kingdom, we always ride the Jungle Cruise, Peter Pan's Flight, Mickey's PhilharMagic, and it's a small world. At Epcot, we take in Spaceship Earth, Living with the Land, and tour the countries of World Showcase. Highlights of World Showcase are the Kidcot Fun Stops, which are craft stations where children can draw and color while learning about different cultures as they interact with Cast Members from around the world. Our must-dos at Hollywood Studios include Toy Story Mania and Muppet Vision 3-D. At Animal Kingdom, our family always rides the Kilimanjaro Safari and visits The Boneyard and Conservation Station. Of course, every family is different, and to have a successful trip, you will have to take your daughter's likes, dislikes, and comfort-level into account.
Also have a look at Disney's in-depth planning page for
traveling to Walt Disney World with younger children. As you enter the parks, pick up a Times Guide for parades and show schedules throughout the day. During your visit, you can't go wrong with a character meal, particularly at Chef Mickey's or Cinderella's Royal Table.
My best advice is to relax, follow your daughter's pace, and enjoy.