Our first trip with our daughter was last September and she was 19 months old. She loved it and had a great time. We did too!
I sometimes think it's more a question of not if the child is ready to go, but if the parents are (especially on the first trip), cause it's a whole different (but better) experience in my opinion when you go with kids. You need to do the parks at the kids pace, not yours. You need to take nap breaks, have snack times, etc... Heck, we found nap time back at the resort quiet nice for us growns-up too actually!
We originally didn't think of going until DD was 3 years old for own sanity, not hers. But we opted to give it a shot and it was completely fine. We had a blast with her and she loved seeing all the characters, going on the rides, etc...
She's 27 months now and name every major character and princess and we're looking forward to taking her again in September this year.