Hi Jennifer!!!
We first starting taking our son at six months old so I can totally relate with your question!!!
There are a lot of attractions that your 15 month old can experience at both the
Magic Kingdom and
Disney's Animal Kingdom. I figure the best thing I can do to help you out is list out all the rides that your 15 month old can do at each theme park.
The Magic Kingdom is definitely geared towards the little ones as it has the most attractions your 15 month old can experience. You can ride/experience the Haunted Mansion, Mickey's PhilharMagic, Buzz Lightyear's Space Ranger Spin, it's a small world, Dumbo The Flying Elephant, the Jungle Cruise, the Liberty Square Riverboat, Mad Tea Party, The Magic Carpets of Aladdin, The Many Adventures of Winnie the Pooh, Monsters, Inc. Laugh Floor, Peter Pan's Flight, Pirates of the Caribbean, Snow White's Scary Adventure, Tomorrowland Transit Authority Peoplemover, the Enchanted Tiki Room, and the Walt Disney World Railroad. As you can see, there are a lot of attractions you can experience with your 15 month old at the Magic Kingdom.
You would be able to experience/ride the following at Disney's Animal Kingdom: Kilimanjaro Safaris Expedition, Festival of the Lion King, Finding Nemo-The Musical, It's Tough to be a Bug, The Boneyard, TriceraTop Spin, and the Wildlife Express Train, which leads to Affection Section and Conservation Station!!!
I definitely believe that you will have a wonderful time now knowing all the attractions that your 15 month old can experience and enjoy!!
Please let us know how else we can help with your Disney Vacation Planning!!
Have a magical trip!!
Scott