FYI - we couldn't do the cat in the hat with an infant either.
The list is great, but we couldn't do anything in the Seuss area except the playarea with a "non-walker" - maybe it's different now, but I did look at restrictions before we went and I was under the impression he could do all of them, and he couldn't. The trolley ride is newer but there is a height limit on that.
A lot of things on the list are play areas and shows. Be sure to look at the attraction list on the website to give you an idea of what is on the list and compare it to the list in general and decide for yourself how much you can do with an infant and a toddler
The first time I went with an infant and toddler my expectations were too high. The second time with a toddler was much better, despite rain, and I know it was because I went with different expectations and of course, that time I didn't have a "non-walker"