My friend says that Floating islands are in pre-hardmode, but I can't find them. Do floating islands exist in pre-hardmode?
World generation happens when you create the world, which includes generating floating islands
By the time you have found the angler, the floating islands already exist
The quest you received is not to kill something, but most likely to fish for a Angelfish, Cloudfish, Clownfish, Fallen Starfish, The Fish of Cthulhu, Harpyfish, Pengfish, or Slimefish
Do note that the Angler's quests reset each morning at 4:30am in-game time.