Unfortunately, adding the dragon egg to your inventory and trying to hatch it in the overworld isn't possible in the base game, and you'll need to install a mod to add that ability to Minecraft. In other words, dragon eggs can only be hatched if you're playing a modded game.
The Call of Duty games are on the Gamecube, Xbox, PlayStation, PlayStation 2, PlayStation 3, PlayStation Vita, PlayStation 4, PlayStation 5, Xbox 360, Xbox One, Xbox Series X, Xbox Series S, PC, Nintendo Wii, Wii U, and the Nintendo DS.