Another one with a fun "show" is Restaurant Marrakesh...they have a belly dancer, and invite people up to dance with her....a one year old may be too little to participate except in the arms of a willing parent...but having all that music and activity going on might make it easier to keep them occupied.
Maybe Coral Reef because there is an entire wall that is a glass aquarium and that too might keep a little one occupied.
I'd probably stay away from Le Cellier, as it's dark and intimate and slower paced, non of which are particularly kid friendly, lol.
If the toddler is a girl and enjoys Princesses, you might try to get in at Akershus for the Storybook Princess character meal. The food at lunch and dinner is not typical American fare, but there is a buffet portion that will have a few things that toddler can eat like fruits and cheeses and such. We enjoyed the different foods, but I know some people stick to breakfast here because of the atypical foods at the other meals.
There are MANY wonderful CS meals in Epcot that should satisfy a parents need for something beyond burgers and pizza (which is about all you'll find at CS in DHS)...and of course CS tends to be a quicker meal so that is better for the toddler. If you're on the dining plan though you can't trade TS for CS so that may not help...but without the plan, I personally would probably do mostly CS meals in Epcot with a little one, as I love the variety!