Hi Kelly!
There is so much fun for a 1 year old at Disney World! I've taken my kids at 7 months and 9 months...they don't remember it, but I sure do!
One of my favorite things we did (and this just depends on your kids' head)...is getting their first haircut at the Harmony Barber Shop on Main Street in Magic Kingdom! They make it a truly special event with pixie dust and a "first haircut" Mickey/Minnie ear hat!
As far as attractions? Your 16 month old will love all the shows and parades because there is just so much to look at! I specifically remember my 7 month old son watching the Festival of the Lion King at Animal Kingdom. And my kids have always loved the Disney Junior LIVE show at Hollywood Studios. So, check out a Times Guide at each park for the shows.
A few rides---Dumbo, Small World, Seas with Nemo and Friends, Kilimanjaro Safari. There are also playplaces at every park--my kids love the Boneyard at Animal Kingdom.
Don't forget to check out
Traveling with Little Ones--lots of good tips!