Once you feel comfortable leaving the house with them and taking a trip to a place with many people, that is how old they have to be. It can be different for everyone.
My oldest went to WDW at 8 1/2 months, 23 months, 29 months, and just shy of 3 years old. Then VB when she was 3, and 2 more times when she was 4 years old. (total of 6 times so far.)
Her baby sister was 7 month and 9 months, her next trip will be Jan 2006 and she will be 17 months old. I think it will be harder then her 1st 2 (she was a pretty easy baby, she loved WDW.)
I must admit that I am looking forward to this next trip with my oldest, she will be just under 5 years old (for a total of 7 trips before she turns 5 years old, I think, we loss track.) Each trip gets better and better for her. She enjoys different things and gets different things out of WDW at different ages.
BTW DD who is now 4 remembers every trip to WDW, but her 1st one. She likes to look at the pictures. It doesn't mater if they remember it, we won't ever forget it. Parents don't stay home until kids are old enough to retain memories.
Have a good time, take lots of pictures. Tolders can be challanging, but if yours is one that can handel it, (or better yet if you are a parent that is up for it, and maybe has some help.) go for it.
Promise it won't be the only time to take her though.