I have a 6 and 8 year old who have been going since they were teeny infants. I have to agree, it's easier taking a younger baby then an older baby. Maybe even easier then my 6 year old
. Every stage has it's challenges.
Anyway, if you are well prepared and have realistic expectations (as in any Disney trip) you will be fine.
I agree with alot of what other posters have written. Definately rent a stroller from an outside comany. Disney strollers are expenisive and not appropriate for a 4 month old.
Take advantage of the baby care centers. Not only are they a great way to relax and cool off, they are so cute inside and have everything you need. I was even able to purchase formula (expensive formula) when someone *cough cough my husband* left the formula in the room.
Another thing that I have always done is send down a package via UPS to the hotle we are staying at so I didn't have to pack all the baby's gear. We sent down diapers, swim diapers, formula, the carrier, snacks for my toddler and us, extra bottles clothes etc. Sending stuff down ahead of time is great. You can send it right to your hotel and they give it to you on check in. Saved alot of luggage space and hassle.
If you do use formula-I always kept a bottle of water on me and then I wold go to any counter service/restaurant etc and ask for hot water (like for tea) and then I would use that in combination with the bottled water to get a perfect temp for my kiddo. I was never charged for the hot water.
Lastly-enjoy. Take it easy and let your baby take in all the wonderful sights. Disney isn't going anywhere so try not to rush and be stressed. Congratulations!