This was our experience. I have no idea if this is usual; it's just what we encountered.
We took our oldest when she was 5 months, and then again at 16 months. The first trip was a large family trip that was planned before I knew I was pregnant. We were there the week of Christmas. I was nursing, so no need for milk or formula. That being said, I learned to nurse on the go whenever I needed to, because the family/baby stations were often on the other side of the park. When they were close, they were convenient -- clean, quiet, etc. We had a large jogging stroller, and it provided all the privacy that we needed for diaper changes. It also laid flat, so she could nap. Half of the time, I wore her in a carrier, and she was super happy. Diapers were not an issue. Our issues were late reservations (or table reservations in general), any activity after 7 pm, fireworks, and some characters (she was super frightened at Tusker House, and on the safari). We did ride switch but she always seemed to be eating when it was my turn. She slept through Cinderella's Table, Hoop De Doo Review, and Biergarten. All in all, it was a nice trip but we had to deviate from our plans, and we didn't spend as much time with the rest of the family as we would have liked, because they were at Fantasmic, etc.
The second trip was also in December. I was pregnant with #2, and she was in full-on toddler mode and could not be contained. She slept through every character meet and greet, threw fits, and barely made it through restaurants (and we take her out to them weekly, so it wasn't anything new). Diapers were difficult, because she was too old to be changed in the stroller. The milk situation was also difficult, because she needed special milk (soy) that was not available at the parks, and it was hard to keep on ice. We bailed on the last day and spent time at the pool. After that trip I vowed that we would only return when #2 was out of diapers. Lucky for us, she potty trained fast, and we are headed back the week before Christmas.