traveling with an infant is a challenge, but very manageable. i agree camcolt's tips, but thought i'd point out that you don't have to bring your own stroller...
dcl has jogger-type strollers available (last i knew, free of charge) on board for you to use throughout your cruise. there aren't many, so as soon as you board, head across the lobby and check with guest services to borrow one. the only problem is they are big and hard to store in your stateroom. we just left ours tucked into one of the areas (you'll see what i mean when you board) outside our stateroom.
we have used flounder's reef several times (two different cruises) and heartily recommend it! as soon as you can after boarding, go to the reef (on deck 5) and check him in. you will be asked to prioritize the days/times you want to use the reef and then they will contact you day-by-day to let you know if he has a reservation. what we did to ensure our ds was in club when we wanted to do palos was use our walkie talkies...dh was getting palo ressies while i was signing into club. he let me know which night, so i made that our priority #1.
ask your stateroom steward for a diaper genie. we didn't know until our last cruise that they have them available. you should already requested a pack-n-play with your reservation, but if you haven't, just call and have it added. you'll probably still need to ask your steward for it, but at least it'll be in your record.
if you need anything warmed at meals, ask your servers. they're very good working with the little ones.
bring his bathing suit and swim diapers. the "ears" in the mickey pool are the perfect depth for sitting with baby in your lap and relaxing. and since they are smaller, there's less chance of problems. the kids will still crawl in and get rough, but we just pointed out that i had a baby in my lap and they would settle down.