Hi, Megan! Welcome to planDisney.
It's an honor to help a fellow Guest plan their next adventure to The Happiest Place on Earth. My wife and I have enjoyed bringing our kiddos on Disney trips since they were tiny Mouseketeers. There are plenty of rides that are practically perfect for wearing your little one in a baby carrier. Disneyland Park is my favorite park for young kids. Here are some attractions that don't have a height restriction and also should allow you to put your baby in a carrier:
"it's a small world" - a slow, gentle boat ride that takes you through delightful scenes showcasing and celebrating the world's various cultures. Warning: prepare to get the song stuck in your head for the next 37 years.
Dumbo the Flying Elephant - an aerial carousel ride that allows you to control the height of the elephant. My kids absolutely love it!
Peter Pan's Flight - an aerial pirate ship ride that takes you through the magical scenes of this classic story.
Jungle Cruise - a hilarious boat ride across the exotic rivers of Asia, Africa, and South America.
The Many Adventures of Winnie the Pooh - a whimsical trip through the Hundred Acre Woods in an oversized Honey Pot.
There's also Alice in Wonderland, Mr. Toad’s Wild Ride, Snow White’s Enchanted Wish, Pinocchio’s Daring Journey, King Arthur Carrousel, Mad Tea Party, and Pirates of the Caribbean.
In Disney California Adventure Park, there are far fewer options.
The Little Mermaid - Ariel's Undersea Adventure and the
Red Car Trolley do permit baby carriers. While most other rides in the park don’t allow babywearing, some—like Toy Story Midway Mania!—allow babies to sit on a parent's lap.
Be sure to check with a Cast Member if you're unsure about a specific ride! I hope that's helpful, Megan. Thanks for choosing to be our Guest.
Mike