Hi Barry,
I remember taking our daughter to Walt Disney World when she was very young and we did not need to contend with school schedules. This gives you a great amount of flexibility. Overall, I would suggest going when most children are in school. This means avoiding most of June, July, and August, the month or so around Easter and Spring Breaks, as well as times close to Christmas and New Year's. Let me give you two specific recommendations for times to go.
The first would be February. Earlier in February can be a bit cooler, but that can be a bonus with a little one! With high temperatures in February around 74 degrees Fahrenheit, you and your child will be quite comfortable in the theme parks; however, it may be a bit chilly for the pools. Avoid Presidents' Day weekend as it will likely be a bit more crowded. Our very first trip ever with our daughter, when she was 7 months old, was in a February.
The next, and my favorite, would be September. Wait until after Labor Day, as it may be more crowded then. In September, children have just gone back to school. It is warmer in September, with an average high of 90 degrees Fahrenheit, so if you are looking to go to the pools and experience warm Florida weather, this would be a good time to go. Also, if you go a little later in the September, there are some great special events at Walt Disney World, such as
Mickey's Not-So-Scary Halloween Party, and the
Epcot International Food and Wine Festival.
I hope that this gives you some ideas on when to plan your vacation, Barry. Please do not hesitate to ask if you have any further questions!