Best timing for 1st trip -- old enough to need no more than one nap, can verbalize what they like and don't like, and eats tables food... but not so big that they don't fit in a stroller!
That puts you somewhere around age 3, I guess!
Seriously, we have taken ours since 8 mos. With a baby, you just realize that it's YOU that is getting the real kick out of this, because they could be just as happy laying on the hotel bed kicking up their heels, so long as there is a face that responds to their actions! At age 1 and 2, you run a risk of the character-fears, quick melt-downs approaching nap-time, and of inexplicable struggles (those lovely power struggles of a 2 yr old where they know what they want but it just comes out as "WAHHHHH! No NO NO NO..."). thankfully mine never had much of this -- they were pretty good with the characters and WDW cruisin' from the get-go, but then, maybe I look like Goofy so they were used to it all, haha. Just tellin' ya what I've seen as a Mom in the Disney trenches.......
At ages 3-4, kids fit nicely in those WDW strollers -- which is a BIG plus, because you can get from point a to point b a heck of a lot faster this way, and their little legs get a rest, and also -- you have somewhere to stash your little cooler with a drink or lite snack for the nipper. My DS is literally crying this year because he knows that he and his brother will NOT FIT and must WALK -- oh the tragedies of a 7 yr old.
A 3 to 4 yr old recognizes the characters, has favorites, and can also verbalize who he/she does NOT want to see (my eldest at age 3 loved Pooh beyond all reason but had a complete freak-out phobia over Eeyore.. knowing this allowed us to clue Eeyore in on the deal in advance, so that he just stood wayyyyyy back at the breakfast and waved sadly from a safe distance!)
Our dd was 2 on our last trip -- and she had a great time, I know, but she recalls very little about the trip, other than what she sees in pictures and says, Hey, there's ME! She tired quickly on that trip, as I recall, especially if a wait was involved. For our visit this August, she will be newly-turned 4 yrs old. She has already decided with whom she would like to dine, who's autographs she wants, and what rides are on her "must-do" list. And whether or not she will have her "own" WDW stroller or share with her cousin. Should be interesting!