I have to agree with the above poster. 1 is sort of an annoying age to take a baby to a place like WDW.
I have two kids. The oldest is 2.5, youngest just turned 1. We live 15 min from
Disneyland Resort and have AP's and go very often with both kids.
The one year old has been very difficult to take to DL in the past couple months and our time there has been more stressful than fun. We mainly go for the older one, who LOVES DL (always has), but his little brother can be sort of a downer (I mean that in a joking way).

He is a very moody baby, has been teething molars for 2 months and has been VERY cranky and sleepy (growth spurt at 12 months). We have taken less day trips to DL for the past 3 months overall and I have taken my older DS alone while DH stayed home with the baby since I can get SO much more done when it's just me and older DS.
At one, babies HATE being confined to strollers. Our oldest walked at 10 months and he hated strollers even more than our 1 year old (who is not walking yet) does. In general, they don't like to be confined for more than about 10 minutes at a time. If your 1 year old is already a good walker, it's no problem to let them wander until they get tired once in awhile.
On the other hand, if you still have a crawler, you can't just let them crawl alongside the stroller, or put them down anywhere. They get amazingly dirty and if the ground is hot, they will burn their hands. In addition, I am "blessed" with a baby who finds nothing wrong with putting EVERYTHING into his mouth, so I have to watch him like a hawk. It's a full time job, I tell you.
Another thing is the lines. You basically have to hold them, and you can have a small one year old, or a huge one. My first is a tiny kid...short and skinny. My youngest is a HUGE baby. He is almost 33 inches long and weighs 25 pounds at 12 months! Carrying him for more than 5 minutes is a burden and a half, plus add in he is always squirming to get down.
If I were you, I would plan the trip for when the baby will be less than 9 months old. 6 months is a good time to go. If you cannot do that, wait until the baby is at least 18 months old. At that age, they are more "toddler" than "baby" and are walking around and being more interactive with people and things in general. They seem to have more fun exploring.
We are waiting until our youngest is close to 2 before we attempt our first trip to WDW. In the meantime, we have DLR, and after only a few hours there, we're beat down exhausted!!!