I want to go to Disney when my child is old enough to remember.....

I've heard this statement more times that I can count. My reply is always "but you'll remember!"  My kids may not remember their first interaction with a character, or the first time they saw Fantasmic or even the first time they rode Pirates of the Caribbean...but I remember. I remember their faces the first time they met Mickey Mouse, had a Mickey bar or Dole Whip, and rode It's a Small World. That look of pure happiness (or confusion, depending on the age of the child). I will always remember these moments....
  Disney has so much to offer for kids age 0-100. Last year we went to Disney in December when Anthony was just 3 months old. He rode in the stroller or the baby carrier and just went with the flow.

(I wore him in the carrier through the lines)

 Traveling with a baby was fairly easy.

A tip: if your traveling with a little one, use the Baby Care Centers, there is one located in each park.  They have a private nursing area with rocking chairs, changing room with changing tables, a feeding area with high chairs, an area with a TV and toys for any other children you may have with you. They also sell Diapers, formula, wipes, etc in case you forget anything or run out.
Also, for Anthony, I found out really quickly that he didn't like the dark rides so I had a bottle ready to go. He would start fussing and I would feed him and it worked out good.

Andrew (the now 5 year old) went for the first time at about 7 months. He was wide eyed and loving everything. He played in the playgrounds/splash pads and rode the rides.

 In case you aren't aware, there are rides that don't have a height requirement.
Pirates of the Caribbean, Haunted Mansion, The Tommorrowland Transit Authority (otherwise known as, the Peoplemover), All the rides in fantasyland, among many others.  This being said, don't be afraid to take a baby to the World if you want to go to Disney. No time is a bad time. Just know that depending on the age of the child, you may need to adjust your touring time. 

Andrew on Toy Story Mania. (I promise, he was having fun!)

Character interaction with kids of all ages is fun! We've had a few moments like this one.

Bottom line, don't be afraid to tour Walt Disney World with small children just remember to take your time, take in all the sights and create wonderful memories with your family!