We took our then 4 month old last fall. She was almost easier than the 3 year old.
We wore her a lot (I like my sling, dad preferred the bjorn as he thinks slings are too feminine). We also had a stroller along for her. She seemed to enjoy the sights & the action of being at WDW. We only did one late evening (had to see Spectro & Wishes), otherwise we got up early (same as we do at home) and were back in our room by early evening.
* give plenty of fluids (formula or breastmilk for a 4 mo old)
* sun protection: hat, shade for stroller, sunscreen, etc.
* duck in to AC attractions, shops, restaurants to keep cool
* extra potty stops--keep that bum dry, especially in the Aug heat
* baby centers are your friend: quiet, AC, changing tables, breast feeding areas (some private, some semi-private), supplies like diapers, pacifiers, etc for sale.
* don't think just because he or she is a baby that they won't notice or enjoy what is going on.
* expect people to want to talk to you more than usual, cute little babies make everyone your friend. (our baby stared and blinked slowly at passersby until she could trap them in her tractor beam eyes and pull them in for a little more attention). Seriously. She is such the flirt.