We LOVE cruising with our four kids (ages 3, 5, 8 and 11.) Our last one was in May and we finally got it right!!!
Get an over the door shoe organizer (less than $7 at Wal-Mart.) Someone gave me that advice and it was, by far, the best I've gotten! You will have a ton of stuff to keep organized in a tiny space (unless you have load more money than us and are in a super-suite!) We never had a problem finding the kids shoes- which we kept on the bottom so they could reach- our sunglasses, lotions, jewelry, toiletries, hair accessories, you name it!
Bring Children's Tylenol at the very least. You might consider a cold medicine and anti-diahrea (sp?) medicine just in case.
Dinners in the main dining room can literally last hours. Not sure what cruise line you are on, but it could be a problem if you are seated with people you don't know. If you have a table for your own family, you have more control of dinner... order the children's meals first and ask that they come when your appetizers come. Then, let them eat dessert as you eat your entree. If they are still behaving, go ahead and order dessert for yourself or else BAIL! BY THE WAY, you are totally allowed to order food for your child off the adult menu! It took us a while to figure that out, but I don't let my kids eat pizza/chicken nuggets/mac and cheese nonstop at home, so why on the ship? My kids enjoyed having steak or whatever for dinner instead of frozen kid fare! Also, since mine are older, it was an opportunity to try out things to see if they liked them and not get upset if they didn't eat it (as I would in a restaurant if I spent $25 on an entree!)
Some budget-conscious ideas... Buy a few cheap inflatables (we got $0.88 rings at Wal-Mart that the cruise ship actually charged about $8- the same exact item!) They are pretty strict if your child is not potty-trained. Buy some flavored drink mixes (the kind you add to a bottle of water to make lemonade or whatever) and save on buying sodas or other drinks... water and ice tea are free. I brought some refillable bottles to bring ashore. Bring some Zone bars or the like for taking ashore... most places ashore are quite expensive. Don't forget to bring sunglasses and sunscreen- the prices for those are crazy if you forget!
Your son may or may not not be old enough to go to the kids club- I think Carnival allows under 2 year olds... my kids LOVED going. Realize that it is customary to tip the daycare workers at the end of the cruise... I brought a thank you note to stick the money in and thanked them personally. I also brought some candy bars to stick on the outside... makes them feel appreciated.
From now to the cruise, save all Happy Meal toys and the like. Bring them and break one out at dinner or when your child is behaving well. This incentive to be good works great and it gives them something to do! (If you wrap them in wrapping paper, you can show it to them when you are trying to bribe them to be quiet or smile for the camera and not ruin it if they don't like the toy- can you tell I've done this before?!!!) Individual packages of gummies can be a life saver too!
Have a great time! Our May cruise was with a group of 30 for my dad's milestone birthday... it's great to have loads of relatives to help watch your child as you visit the buffet line. Consider yourself lucky!