Carnival ships do offer a laundry service. However, they do not do dry cleaning. If you go to the Carnival website, and click on Frequently Asked Questions (FAQ), there is a price list for laundry service. I think they list the prices for washing items and also for "pressing only." There is usually a price list sheet in the cabin. You just complete it, and the cabin steward will handle this for you. Also, I know at least once during a 7-day cruise they offer a "Special Laundry Promotion." The room steward will put a special laundry bag in the cabin with an order sheet. You are allowed to fill the bag and they will wash, dry, and fold those items. I don't recall the prices on that, but it didn't seem unreasonable. I have used their laundry service before, but I try not to have them do any delicate items. I think everything is probably washed in very hot water.
Also, if you are platinum, you can get your laundry done free of charge. Just be careful about delicate items.
Laundry Services In addition to self-service launderettes on each ship, there is a valet laundry service on board; dry cleaning is not available. Following is the price list; this service is handled through the room Steward: