That is a great age to go. Our sons was nine months and, as long as that stroller was going somewhere, he wanted to be in it! My tips:
1. Bring your own stroller. After I took a good look at the rentals, I was glad that we did. They seem to be made for older kids. And make sure your stroller folds quickly and easily for your own sanity, if you plan on using the buses or boats.
2. If you are bottle feeding, you can get bell services to freeze your ice pack over night so that you can put it in your bottle bag with the fresh bottles in the morning. (The ice bucket was fine for overnight bottles.)
3. Make use of the baby centres in the parks. The one at the Magic Kingdom was especially nice.
4. Don't assume that the parks will sell baby food. We had a difficult time tracking down food for him at DHS. Even though there was a sign at the baby centre that they sold it at a certain spot, they didn't and none of the CMs new what we were talking about.
5. I would recommend getting one of those caricature paintings done at your hotel. It's the cutest souvenir of their first trip. (Our son was wearing his Mickey ears in his.)
6.Get a set of baby Mickey ears. Our son wasn't good about keeping his on but once we put them over top of his little baseball cap, he didn't realize they were there and left them on.
7. If at all possible stay at a resort very near Magic Kingdom or Epcot. We stayed at Wilderness Lodge and it was just perfect. So easy to run back to the resort to rest in the afternoon.
8. It's a small world is your friend! Out of all the attractions we visited, this one got the most response from our son. He was captivated by it.
9. Find places to let him crawl around. The Wilderness Lodge lobby was great for this.
10. Either bring or buy a child's sized poncho for when it rains. While a little long, it actually fit our son very well. At first, we tried drapping the stroller with an adult poncho or putting an adult poncho around him. Yeah....no.
11. If you go to the Contemporary, look for the boat they have on the dock. My son enjoyed sitting with me in it and we got some great photos of him "driving."
12. Stickers are fun. In many places, CMs will offer stickers. While we didn't give them to our son because he likely would have eaten them, we stuck them on his stroller to look at. He thought that was pretty cool.
13. Don't shy away from any attraction or evening entertainment. Our son was still a little fussy at that age and we considered skipping many things because of it. We were glad we didn't because he didn't say peep and loved everything.
I hate to leave it at unlucky number 13. If I think of any more, I'll let you know.