We went when my youngest was six months old (oldest had just turned four) and she did great. You do certainly have to be mindful of their needs at that age (really you do with kids at any age), but in a lot of ways it was easier than the trip we took when she was a year old. She slept in the stroller, could sleep in my arms during rides, nursed during dark rides or shows, and in general was very good. Of course she isn't going to remember any of it, but she enjoyed looking at all the bright colorful sights.
When we went with her as a 12 month old, she interacted a lot more with everything, but she was higher maintenance. She didn't really sleep at all when we were out, and wasn't great about sleeping in the hotel room with everyone around, so it was more challenging. Babies need their naps! It was still a fun trip, but a little more tiring for everyone involved. We will be going again in a couple of months, and it will probably be harder still since she is so mobile now.
I wouldn't be afraid to bring a baby in the age range you are talking about, but I would prepare to be flexible and willing to take breaks if the baby (or you!) need them. I personally would avoid going when it's really hot out, just because it's harder to keep everyone hydrated, but otherwise I would say go and have fun!
Disney World is as kid-friendly as it gets, even for babies. Eating at the table service restaurants, for example, is easier than it is in most cities. They will always have high chairs and no one acts annoyed to have to serve a table with little ones, even in the nicer places.