Gardevoir isn't based on an animal, but it does have an origin. Bulbapedia's origin looks pretty accurate to me, so I'll show you that.
Gardevoir resembles a ballroom dancer. Its exaggerated head with minimal facial expression and an overall frail, featureless physique could also be attributed to anesama ningyou, a style of traditional Japanese paper doll. Its protective nature over its Trainer may suggest that it is based on a guardian angel, though its ghost-like characteristics could also suggest that it is based on ghosts that refuse to leave this world. - [Bulbapedia]
The guardian angel one is probably the correct one, as Gardevoir is known to protect it's Trainer according to the Pokedex. It's name also has 'guard' in it, which suggests that this is correct.
Gardevoir looks like a humanoid fairy imo, but that's just me.