we took our son at one, and in May we'll go when he is 1.4. So I'm not used to a big walker yet. You might want to think about places where he/she can walk freely without a big crowd. If you have a child with a big urge to run and roam, I might go to tom sawyer's island (if the raft isn't too crowded).
It is really a great time to take a child, because there is so much developmentally going on that all the sights and sounds and stimulation will really benefit them.
You and your wife have been there before, so I wouldn't over plan, I wouldn't plan on seeing stuff just for the adults to enjoy. I would take it easy and slow and enjoy it from the child's point of view. I'd spend less time in lines and stuff and more time just being and hanging around and looking at interesting things while a fast pass came up. With Holden, we might have ridden 7-8 things a day and were very happy with that. Some days less, just kind of taking it slow.
They have pack in plays in the villas, you can get a crib. There are high chairs in the restaurants, there are changing stations in most male and female restrooms. The baby care centers (near Casey's hot dogs in the magic kingdom, and where the odyssy used to be in Epcot) are good places to get a quiet out of the way time. Your child is probably old enough to eat off of a child's menu, but whatever your child is doing with eating - they are easy going about all things children at Disney so don't worry a second about bringing in some kid's food and having snacks and stuff like that on hand. You'll want a room with a tub, not a handicapped room. If your child is starting to roam a lot be mindful of things like the balcony of course. In the villa you'll have a fridge and that makes things easier, and, at least for our smaller child, the washer and dryer and dishwasher (bottles) were vital. I wouldn't settle on a studio if I had enough points because of things like that.
These are the things that my one year old liked a lot: living seas, the boat ride in Mexico, winnie the pooh. Holden hasn't ridden small world since he was about 4 months old, but he loved it then. Rides that he was OK with but didn't really love, just liked them so-so: peter pan, pirates of the caribbean, haunted mansion, buzz lightyear, people mover, train, journey into imagination (watch out for explosion at the end), jungle boat, living with the land. Wasn't a big fan of Mickey's philharmagic (loud). Holden liked the tea cups a lot. He enjoyed country bears a good bit, but not as much as I thought he would (I thought he'd just go nuts, because he really likes music and dancing). The tikki room was OK, but gets a little intense at the end - Holden liked looking at the tikki gods. That is about all we've had him on, plus a couple of shows.
Now listen to this. You are right at Dumbo age. So - depending on your child of course, and if you have an early enough riser - you want to go to magic kingdom either first thing on an early entry morning and head straight to dumbo, or first thing on a non-early entry morning and head straight for dumbo. You probably don't have to worry about the autopia speedway cars yet, but you probably want to get to Dumbo first thing.
Fantasyland is your land, by the way.
Oh, you really should go to playhouse disney in the studios. We didn't do a lot in the studios with Holden, but I wouldn't miss that one if you ever let your child watch playhouse disney shows. Also, Jo-Jo from Jo-Jo's circus is at the studios, that might mean nothing to you and it might be a major huge deal, depending on if you let your child watch the show.
You really should do a character meal. We didn't ever do them before we had a kid, but they are great for children. Holden loves them. The characters are pros and know what they are doing and are really sweet with the little ones. If you are just taking your time, you'll probably run in to some characters in out of the way places. I remember seeing sleeping beauty down by the international gateway one day, and she sat on the bench there and talked to Holden for a while. Also, this is going to sound kind of weird, but I think the meal that Holden enjoyed even more than characters was 'Ohana. He just really loved the music and singing, and I think the excitement of the kids doing things like coconut races and hula hoops, he was laughing and clapping and dancing the whole time, completely happy. So we thought the music thing was the big key to eating, and so we tried the german buffet with the oompah loompah band the next night, with lackluster results.
Thinking about characters, here's another tip. After you go see dumbo first thing, check the guide maps to see what time Mickey's house in toon town opens. It will probably be after the whole park opens, so if you go there right when it opens you will be able to see Mickey and the other characters and get some photos without a long line or feeling like a lot of people are waiting behind you.
But - despite me saying that you should be there early for Dumbo and Mickey - be sure to just take your time and do it on the child's pace. Let them enjoy it. Let them get wet and play in sprinklers. Let them crawl around on the lights in the sidewalk in epcot at night. Let them take long naps. Let them swim with you in the pool and play with whatever water features are there. Try to see spectro magic - the lights and the music are wonderful for young ones. But if it is the only night of the week that the parade is showing know that it will be a huge crowd and it might not be worth the hassle - you'll have to guage that one. But wow is it great for little ones. I wouldn't worry about fantasmic yet. Others might disagree, but I think fantasmic is aimed squarely at the preschool set, not the best for toddlers when you factor in the waiting and crowds and everything. We've always been a little iffy about fireworks for Holden, on our last trip he say illuminations, and wasn't scared, but wasn't really wowed either (spectromagic is a major, major, wow for him, in comparison). Your child might be different. Take time to walk through things like innoventions, living seas, the animation building, that is fun for the child to look at and play with.
Animal Kingdom hasn't been our top priority for a very young one. We had a lot of family down last Oct. and he rode the safari ride and liked it OK, but wasn't blown away or anything. For him, it is just as easy to skip it for now, save it for the preschool years. I would be just as tempted to skip the studios, but he really liked playhouse disney.
Here's something fun. Do you know on main street right next to Tony's Town Square there is a kodak photography place. You can go in there and take pictures, and they'll place them on backgrounds (like different scenes with characters) and you should probably think about doing that. But if you keep walking straight back, and take a right turn, there is one of the old mr. toad's wild ride cars that you can sit in with your child and take a photo. There are some other photo sets, like a black and white steam boat willie, and a TV with the 101 dalmations, that you can take photos with. Just slow down and have fun with things like that. Take a picture of your child next to the cigar store indian so that you can take another one next time you come and see how much you grew (or Humphrey bear if you are at the wilderness lodge).
Also, listen. Don't think twice about a stroller. You might agree with me that back when we were childless strollers seemed out of control. Well, you don't have to commit to a land barge to carry all your worldly goods in, but you'll want one. Also, don't be surprised by all the stuff you have to take with you to the parks, or all the stuff you have to pack to get down there. You are one of those stroller people now, you'll just have to accept it.
But mostly just have fun and enjoy your child enjoying the things around them. If I think of something else I'll let you know. Have fun.