SUNSCREEN!!!.... If your baby is not old enough to safely wear sunscreen, please wait to go to WDW until he/she is!
Sunhat... a definite must! Helps shade the sensitive eyes from the sun, as well as protect the scalp from sunburn.
Shade.....make sure to have a lightweight cover to drape over the carriage, and make sure that those little legs that are sticking out from under it aren't getting burned. I have seen absolutely hideous burns on children because a leg got out from under that shading.
Hydration... make sure your baby is getting more hydration than you would normally give. It is quite hot down here. Make sure that your baby is wetting the same amount of diapers that he/she would at home.
Strollers...
Rent a stroller or bring one. The baby backpacks/slings are fine for a short time, but factor in the body temperature of 2 human beings and the hot, humid Florida weather, and overheating can easily occur. While in line, or in an air conditioned pavillion is great, but the stroller/ carriage is a much better alternative while outside.
Dress your baby according to the weather.... If you are hot, he/ she is as well. Bring a lightweight blanket to cover them while in air conditioned attractions or buildings.
Food... baby food, formula, diapers are difficult commodities to come by while in WDW and extremely expensive when you do. Formula and baby food are not available at Downtown Disney, as so many seem to think, and the diaper kits won't fit children under about 20 lbs. If you have a car, Goodings (a 24 hour grocery store) is at the end of Hotel Plaza Blvd on SR 535, but you will have to drive, or take a taxi to get there.
Baby meds.....Also, remember to take baby Tylenol, or any other types of medication your child may require with you, as they are also very expensive on property, and may not be even be available.
Overload... WDW is overwhelming to adults, can you imagine what it must be like for a baby? Huge furry characters with big faces? Don't thrust the baby in a characters arms. They could be traumatized, and it wouldn't make for a very enjoyable experience for anyone.
Downtime... take it! It is best for everyone's sanity. There is nothing worse than seeing a baby crying, and hearing the parent telling it to be quiet, because they paid to be there. The baby is too young to understand that type of reasoning. All he/she wants is familiar surroundings.
Hope this helps.