We just did it and I am not going to lie, our 18 month old was tough. But it is personality dependent, he wanted to walk and got annoyed with the stroller. Our fix was one of those back pack harness (dare I say leash). He loved that thing, gave him mobility and freedom but kept him safe. Never thought I would use one, but it was a huge help
It really is. My youngest was 16mo on her first trip and she was a breeze! There was so much to interest her that she was constantly distracted, the crowds made her just nervous enough to prefer the stroller over walking 98% of the time, and she just adored all the sights and sounds. She's more difficult now, at 4, because she's got all these opinions about everything - at 16mo she was content just to take it all in.
Some general tips - a good stroller is a must, and by that I mean something that folds easily, preferably to a relatively small size, and has a decent recline and generous sunshade. We travel with a Peg Perego P3 that I just adore - folds down like an umbrella stroller but reclines like a full-featured model, and has a sunshade wide enough that with the seat upright the shade comes all the way down to the lap tray.
Get an hourglass shaped sippy or straw-cup that closes, and make or buy a "leash" for it to attach it to the stroller. WDW is hot and you'll want something your little one can sip on often during the day without having to stop and dig it out of a bag every time. And if your toddler is self-feeding with utensils, take-and-toss silverware is indispensable - that familiar child-size and managability at a price where it doesn't matter if a few pieces get lost. I paid $3 or so for a 12 pack that was half forks, half spoons. And to go with those things, grab some pre-soaped sponges or make them yourself (wet sponge, work soap in, allow to dry completely, cut into quarters, pack in ziplock baggie) to have for evening clean up.
Also, if you haven't already discovered this with your older kids, triangle crayons are the best thing since sliced bread. Sure, Disney will give you crayons with a kids menu but how many times will you be on the floor under the table retrieving them? Crayola makes them, but check the dollar store first - I've never had to pay Crayola prices for ours.
We had a blast taking DD on her first trip when she was so young. I have the sweetest picture of her watching the castle show with such a look of wonder on her face. It really is one of my very favorite mommy-memories.