Does the Changeling ability count for Happily Ever After?
No, that won't work. Creature types are subtypes and not card types.

205.2a The card types are artifact, conspiracy, creature, enchantment, instant, land, phenomenon, plane, planeswalker, scheme, sorcery, tribal, and vanguard. See section 3, “Card Types.”
205.3a A card can have one or more subtypes printed on its type line.
205.3m Creatures and tribals share their lists of subtypes; these subtypes are called creature types.

In regular games, you'll only see artifact, creature, enchantment, instant, land, planeswalker, sorcery, and finally tribal (which is never encountered alone, but always in combination with another card type).