Hi Hilary,
Traveling through World Showcase with a three year old can be a fun, relaxing time for your family. From my experience, three year olds are usually fairly content to sit in their stroller and take in the scenery, especially if you've been going at a non-stop pace during your Disney vacation.
Agent P's Adventure is a lot of fun, and a great way to get kids excited about World Showcase. Will your little one like it? I don't know. The great thing about it is, you can sign up, get your mission and end at any time. If you find you don't like it, just take your F.O.N.E to the nearest Agent P kiosk, and a cast member can end your mission.
Illuminations is beautiful, but it is a late night. After the show, huge crowds exit the park. It can make for a long night with a tired little one. I would skip it this trip, especially since you want to get an early start the next day.
There are a ton of characters to meet in World Showcase. Check your times guide when you get to the park, but you'll be able to see: Donald, Mulan, Aladdin, Aurora (Sleeping Beauty), Belle, Snow White, Alice in Wonderland, Mary Poppins, Winnie the Pooh, and others.
Look for
Kidcot fun stops. They are stations located in most pavilions where little ones can decorate a cardboard Duffy the Disney Bear. Cast members share information about their native land (such as how to say hello) and give your child a stamp of Duffy. Stopping at one or two of these would be fun for your little one.
Hope this helps. Have a magical vacation!