Other than sharing the same sprite with Shanghai Doll, the doll has no official artwork.
Varying means of differentiating Hourai from Shanghai in fan works include depicting her wearing a bonnet instead of a hair bow, wearing a red dress instead of a maid outfit, and depicting her hanged (cf. spell card name "Hanged Hourai Dolls"). Some stick to the sprite and hold it that Hourai looks completely identical to Shanghai.
Just as with Shanghai, it is a possible interpretation that Hourai is a type or class of magical dolls rather than an individual doll.
Hourai has become a relatively popular supporting character (or artifact) in Touhou fan works, even though in-game they are indistinguishable from ordinary Shanghai dolls.
Fujiwara no Mokou's spellcard "Hourai Doll" is completely unrelated.