We took our son and my parents to DW when he was 12 months, 18 months and 24 months. The first thing I can tell you is RELAX.
There are tons of things that he will be able to do. The biggest piece of advice I can give you is identify the MUST DO things ... do them and then relax. We were fortunate in that we had been many times before and when we took our son we simply went with the flow.
A few must do things....
1) Do priority seatings for some meals. Depending on the time in June it can get very busy. We went the same time and it was busy. We would pick one "character buffet" a day and make a PS for it. If we made it fine, we had a place to eat, if not, no big deal. Some of our favorites and our son's were: MK -Crystal Palace (Pooh, Tiger, Eeyore, Piglet) for lunch or dinner; MGM - Holloywood and Vine (Minnie, Pluto, Goofy, Chip/Dale); Chef Mickey's (Contemporary) - Mickey and gang; MK-Liberty Tavern (dinner) - Minnie and Gang; Ak-Rain Forest --no characters but the animals fascinated him...the thunder storm scared him at first but we told him it was the angels bowling and he got a kick out of that.
2) Plan time in the afternoon to go back to the room and let him nap. Often my parents were ready for a rest and would watch him in the room while we went swimming.
3) Plan time to go to the Disney Marketplace. Bring a couple extra pairs of clothes and let him play in the different "water" exhibits. He will also love the
lego shop where he can play with those. And guess what, McDonalds is right there.
4) Bring your own stroller. My son would often take a nap in the stroller. We would simply go into an air conditioned restaurant and let him sleep while we sipped on a cold pop and relaxed.
5) Don't miss Toon Town and the little playground there. It is smaller than the one at AK and our son had a good time. Plus, he could do most things there like Mickey's house, etc. He loved sitting in the cars and pretending.
6) Fantasy land was, of course, a big hit. We took him on Peter Pan and he liked that...hold onto him tight. He LOVED pooh, dumbo and most of the other rides. Snow White was pretty scary for him. I covered his eyes in some things and played peek a boo... The lion king was a bit long for him. He also loved Country Bear Jamboree in Adventureland.
7) Bring a cotton hat, one with a flap that goes on the back and shoulders. When he gets hot you can dip it in water and put it on his head. Also, we bought small, clip on fans that were battery operated. We connected one to each side of his stroller and he had a breeze most of the time. Encourage him to drink lots. We often diluted juice with water and he didn't notice. That way he got the liquid without all the sugar. I think it was at DW that we bought snow cones without the syrup and he liked the ice.
The best piece of advice is to enjoy. Don't stress out if you don't get to see things. You might also want to buy one of those two-way radios for you and your parents. That way, if you get split up, you can easily find each other. That or cell phones work, too.
8) The fireworks often bothered my sons ears so I would simply play "hide and seek" with his ears and he thought that was funny. He liked all the lights.
9) Be sure to go when it is dark. My son really got into the lights.
Good luck. Let me know if I can answer any questions. We've stayed at the Dolphin but it was before my son was born so it has been awhile. You will enjoy yourself.