I'm assuming its the same on RCCL as CCL, and if it is, there is an iron available in the self service laundry areas on the ship. You could use it, but you then may have to worry about waiting to use it (on formal nights when everyone wants to look their best)
As for the hairdryer, yes they provide one, but as others have pointed out, they are not the fastest working hair dryers. If you decide to bring your one you should also bring a small extension cord for it so you are certain you can reach a mirror while drying...
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013