I, too, took infants to the Park--although toddlers are much more fun!!
Babies are a lot of work, whereever you are--but some preplanning can make it a very enjoyable day and you won't have to be worried about how he is , ect....Distilled water and powdered formula (which he has become accustomed to long before the trip)will be a big help, as well as a variety of sealed baby juices,a steady supply of Cheerieos and a favorite powder to help combat heat rash...several changes of clothes will help with that as well...and sunscreen!!!
if he has a favorite musical toy that he is used to napping with, it can sometimes drown out all the extra unfamiliar noise and help with the needed rest. There are shaded spots throughout the Park (I used the Gazebo in Frontier Town or spots along the Trail--though the Force may make that obsolete..)
Another thing that worked for me was to take a blanket and stretch it out on the grass back in Frontier Town so he can move around a bit. The pace is much different with a tiny one--isn't it with everything? I also tended to backback mine that needed the contact, or perfered to be more upright, though by the end of the day,,,,
over the years I have taken more than 20 little ones (under 5)though never more than 8 at a time.. and have enjoyed each trip! Good luck!