Hi Alisa!
As someone who has brought his son when he was 1 and 2, and daughter when she was 3, I certainly empathize with the question (smile). Before leaving the resort room, I would equip myself with every possible item I could find in case there were any meltdowns. Toys, favorite small snack, sunglasses to play with, whatever it took...
I would generally try to bring a toy, or maybe even a coloring book that was still fairly new to them. Since it was dining, it wouldn't be a toy that made a ton of noise or spun (Disney has all those great spin toys, but my children would have 'found" that small glass of drink when pressing the button-lol).
If you have another adult, some time you may have to tag team where one eats a little while the other goes outside so the kid can get some energy out.
But the characters are actually great with the toddlers, and get them smiling, which helps when you want to get that extra bite in (smile).
But mostly, for all the magic in Disney, there isn't a magic solution that works all the time. Kid temperaments are unpredictable, and as parents, we just have to do the best we can.
So here's to you, Mom! May your first trip be a magical, memorable, stress-free Disney vacation!