Hi Rebecca,
I would vote for the Magic Kingdom (MK) at that age. Its filled with bright colors which typically appeals to younger kids. Plus there's a lot going on which keeps them entertained.
MK is a great place for character interaction. At that age, most kids are very curious about the characters & aren't afraid of them which can make for some cute photos.
There are many rides that you can enjoy together. Your 1 year old can ride any of the attractions where he/she meets the height requirements (HRs). You can find a list of the attractions with HRs by visiting the
Traveling with Little Ones section on the WDW Website. There you will find a PDF file on the right side of that page that lists attractions at all of the theme parks that have HRs. Little ones love rides like "it's a small world". There are many bright colors & of course the theme song that will stick with you for days.
Be sure to allow your child the time to explore. The Many Adventures of Winnie the Pooh has an awesome interactive queue that kids love. One challenge you may face is keeping your little one entertained in line. Favorite small toys, snacks, bubbles & playing games like peek-a-boo can help.
Be sure to give your little one breaks from the stroller. Try (it will be hard) to stick to nap times & feeding schedules. Take advantage of the Baby Care Centers located in each theme park. Click
here for some tips on strollers.
Be sure to take lots of photos. Your little one will not remember this trip but you can relive the memories with them later through photos & videos. Wishing you minnie magical memories :-) Allison