We went a few weeks ago with our 19 month old and our 3 year old boys. We got a seat for both boys (if you get a seat for a toddler under 2, you do need a car seat).
We take a backpack full of small (quiet) toys, crayons, paper, books and mini-magna doodles. We also take snacks (goldfish, Nutri-grain bars, & other small, non-messy snacks). These seem to keep the kids occupied on our 2 1/2 hour flight. Depending on the time of your flight, you can also hope that your toddler sleeps.
We do take the stroller all the way to the gate, and then check it there. It will be waiting for you when you get off the plane at your destination. The worst part of this is that you'll need to send the stroller (and the car seat) through the x-ray machine, so you'll have to get your child in and out at security.
We did not bring any kind of seat for the meals. All the restaurants have high chairs. In our hotel room, he did okay just sitting in the table chair for snacks & breakfast. We also didn't pack any other toys (other than our plane toys) because there is so much to do at Disney that we didn't need them.
We pack disposable bibs for those messy meals & snacks. We also bring a couple of sippy cups (our son is not very neat with a cup & straw). We pack our diapers and wipes in our suitcase, which leaves some room for souvenirs when we come home, though some people choose not to pack them and buy them there. If your toddler is not potty-trained, you will need swim diapers for the swimming pools.