All 4 of mine made there first trip before age 2. Here's my tips:
Rent a car! the busses are a real pain if you are dragging strollers, baby packs, and tired kids along. Especially if it's late. The other advantage is you can go to Gooding's Grocery (just east of Down-Town Disney) for more supplies (milk, snacks, diapers, and so on). You can buy these things at the parks/hotel, but supplies are spotty, and the prices high. Parking is free for resort guests.
Take you own strollers. Especially good if the kids can nap in them. At the MK, with strollers, we opt for the ferry over the monorail unless it's not busy.
Don't try to change your kid's sleep cycle just to stay late or go early. You'll just wind up with cranky kids.
We like Chef Mickey's and Pooh's breakfast at the Crystal Palace. You don't have to do just breakfast; we do an early dinner or late lunch sometimes.
Don't do too much. Pixi-dust disolves slowly in the blood stream. Relax, do what you can, and don't sweat the rest.
Don't go every day to the parks, we go one or 2 days then take a park-break and explore the rest of the World. There is plenty to do. Some of the other things we enjoy: Fantasia mini-golf (little ones play free), Down-Town Disney, swimming in the pool at the hotel, going to Fort Wilderness (petting zoo, pony rides, beach).
Kid-swap is great. With the extra adult it will work beautifully: no one has to ride alone all the time.
Best bets to be hits with the small ones: Small World, Dumbo, The People Mover (TTA), Buzz Lightyear, The Country Bears, The Tiki Room, The Jungle Cruise, Peter Pan, Mexico, Living with the Land, and the Living Seas.