We took our DD at 4 months, then 15 months, then 20 months, then 26 months...I have to say it became progressively more difficult with each trip, but what you lose in convenience you gain in enjoyment of watching them soak up the fun!
Some things I learned for us, your mileage may vary:
(1) Disney World is loud. When our DD was 4 months we took her on the Universe of Energy...fortunately right before the big bang (the ding dang?) I had the presence of mind to cover her ears...very loud stuff indeed...she slept through the whole 30 minute ride.
(2) the Snuggli is your friend for the little one. I wore my DD for the -entire trip- when she was 4 months. She had good head control so she was facing out and she loved it. She spent 5 days in that thing, start to finish aside from some baby swaps...and we did the parks commando style...if she got tired, she fell asleep, then I would turn her facing in...when she woke up, I turned her facing out again. Most importantly for us, no going back to resorts, no nap time...this rule held even through our last trip - if DD gets tired enough, she falls asleep...then it's time to head to one of the Mountain rides!!
(3) The nursing centers are excellent. Entertainment for the older child, and nice clean, usually private facilities to take care of the younger...and they have what you need for sale if you under-packed something (see #5)
(4) Don't bring an SUV-sized stroller if you're using Disney transportation. We always use Disney transport, and we have a nearly-umbrella sized stroller. It is a piece of cake getting around with a 2 year old and a tiny stroller...on the other hand, we saw some parents getting on the busses with strollers that looked larger (and heavier) than my car, carrying enough luggage for a 3 week safari, and they just didn't look like they were having fun at that point in their lives. Which brings me to...
(5) Bring what you need into the park, and nothing more. For us it is fanny pack (camera), as few diapers as needed, extra pair of pants...if a shirt gets messy we'll buy one in the park, wipes, water, sunscreen...
(6) Kids dry quickly in the Florida sun. One of the highlights of our last two trips were the little water/fountain spots in the parks...just letting our DD get soaked...or trying to convince her to stand over a water jet when you know it's about to turn on..
(7) Don't be afraid to have a 'kid leash' on hand if your kid is a runner. I don't care if a few people look at me nasty or think a leash is cruel...if DD gets in one of those darting moods, she gets hooked up unitl she straightens out and starts listening...There is no way can I get over the turnstiles as fast as she can go under them if she decides to bolt...and there's a lot of powerful machinery for her to get hurt on if she darts the wrong way.
Other people may vacation differently, but I can honestly say for us that we're having more fun with DD along than when we went sans-kids...she goes by our schedule and has an absolute blast, and so do we...if she needs to sleep she is welcome to do so...we actually move faster when she finally passes out.
48 days until our first trip with DS

- he'll be almost 6 months for his first trip, DD will celebrate her 3rd b-day down there...we're not even remotely worried about this trip...with DS in the Snuggli, it will be a piece of cake...
Now the thought of having two walkers...or runners for that matter, that scares me!
brentm3