Our daughter was about 21 months on her first trip (Apr 02).
First of all she enjoyed many experiences, but 3 weeks later did not remember a thing - the trip is more for you, than it will be lasting memories for her.
I second the advise from above - take your own stroller. Take a mid day break. Keep her out of the sun as much as possible, use a hat and lots of lotion.
Have plenty of snacks and liquids with you at all times.
We did go to all 4 parks, but there is not much for a 18m child at Epcot, or MGM. She may like Playhouse Disney show or the Honey I Shrunk the Audience playground at MGM.
Our DD liked some of the things at AK - she especially liked her visit with the Pooh characters. Some toddlers are afraid of characters - ours loved them. AK has the shortest lines of all the parks for visiting characters. She also liked Boneyard Playground and the Triceratops Spin. She enjoyed the Lion King show.
At MK, Fantasyland and Mickey's Toontown will be your major destinations. If you can get up early enough for EMH, go directly to Fantasyland, you will be able to do alot with short lines.
Take advantage of fast pass as much as you can.
If the posted wait was more than 20 minutes we skipped that ride, our DD just can not wait very long. Also she always wanted to be held, standing in line holding a 25lb squirmer for any length of time is no fun for anyone.
Take it easy and slow. The best we could do was 4 hrs in the AM a break and then 3 hrs in the PM.
We stayed at AllStar Movies. She like the colorful Icons. She enjoyed splashing in the kiddie pool as much or more than any of the parks.
Our DD was not restuarant trained. She could not eat anywhere that had more than a 30-40 minute meal, unless she feel asleep. So for us that rule out all the sitdown restuarants - we got food from the food court and ate in the room many meals. If your DD is more used to restuarants, you may enjoy a sitdown meal or two - maybe even a character breakfast, the Pooh characters are at MK - Crystal Palace.
Have a fun trip, just don't over do it.
Jeff