Hi Beth!
Thank you for sending your question to the Disney Parks Moms Panel! My answer would be: it depends! There are rides that may require a seat belt or lap bar which may interfere with the carrier. For example, Dumbo requires a seat belt and Peter Pan's Flight has a lap bar. You would be able to carry the baby, but I am not sure if the carrier would be best. When in doubt, ask the Cast Member located at the entrance of each ride. They will be able to provide assistance or recommendations.
You would be surprised how many rides a little one can enjoy at the Walt Disney World Resorts! My daughter's first trip to Walt Disney World was at the age of 17 days old! She was able to ride many attractions with me such as "It's a Small World", Peter Pan's Flight, Dumbo, and many more! You can view a full list of attractions for all guests (regardless of height) by visiting this page:
Attractions. Be sure to pick the option that says "Any Height"
Here are a couple of "must see attractions" my little ones can't live without: "Toy Story Midway Mania" and “Disney Junior – Live on Stage!” at Disney's Hollywood Studios; "Peter Pan's Flight", "Buzz Lightyear's Space Ranger Spin", "It’s a Small World” and the "Magic Carpets of Aladdin" at the Magic Kingdom, "The Seas with Nemo and Friends" at Epcot and "The Boneyard" play area at Disney's Animal Kingdom! Also, you don't want your little one to miss meeting their favorite characters!
If I can offer any more "Visiting Disney with Toddler" tips, please feel free to send them my way!
Wishing you a great vacation!
Yael