we took DD to WDW when she was just about 3 months old for the first time. it was really easy. at that age, all she did was eat and sleep.
we took her on her first cruise at 5 months (not
DCL though). i never expected to leave her with anyone, which was fine because on the line we sailed there was no babysitting available. again, she did great. slept at the shows and stayed entertained in her carrier at dinner, etc.
it got trickier once she became mobile. on our last few cruises with her (16 and 17 months), she was mostly only interested in climbing stairs and running around! it was still do-able, but we reminisced about the "old days" when she slept all the time and it was SO easy to travel with her.
she is 20 months now and we're sailing on the Wonder next week. I'm sure she will appreciate things
slightly more than when we previously took her to WDW (like checking out the characters, etc). we'll try flounder's one night, but otherwise I expect she'll behave ok on board and have fun at the beach.
for us, it was definitely EASIER to travel when she was smaller (I was also nursing full-time, so we didn't have any bottles to worry about). Now, it's trickier finding ways to make sure she's occupied and happy and well-rested. But, i think SHE has more fun now.
good luck! anywhere between 4 and 14 months should be just fine- it's up to you. be sure to consult your pediatrician if you have any concerns over your child's health. many cruise lines have restrictions on how old children must be in order to cruise.