Attractions you can safely take an infant on:
Magic Kingdom
Walt Disney World Railroad
Main Street Vehicles
Swiss Family Treehouse
Aladdin Magic Carpets
Enchanted Tiki Room
Jungle Cruise
Pirates of the Caribbean*
Tom Sawyer Island
Country Bear Jamboree
Hall of the President's (for a nap of course

)
Liberty Square Riverboat
Haunted Mansion*
It's a Small World
Peter Pan
PhilharMagic
Cinderella's Golden Carousel
Snow White*
Dumbo
Winnie the Pooh
Mad Tea Cups*
Minnie's House
Donald's Boat
Mickey's House
Hall of Fame/Judges Tent
Tomorrowland Transit Authority
Carousel of Progress
Space Ranger Spin*
Epcot
Spaceship Earth
Universe of Energy*
The Living Seas
Living with the Land
Circle of Life
Journey into Imagination*
Honey, I Shrunk the Audience*
El Rio del Tiempo
Reflections of China
The American Adventure
Impressions de France
O Canada!
MGM
The Great Movie Ride*
Playhouse Disney
Magic of Disney Animation
Voyage of the Little Mermaid
One Man's Dream
Millionaire
Narnia
Backlot Tour*
Lights! Motors! Action!*
Muppet Vision
Indiana Jones*
Sounds Dangerous*
Theater of the Stars (Beauty and the Beast)
Fantasmic!*
Animal Kingdom
Kilimanjaro Safari's*
Pangani Forest
All of Rafiki's Planet Watch
Flights of Wonder
Maharajah Jungle
The Boneyard
Pocahontas
Festival of the Lion King
It's Tough to be a Bug*
* Use discresion