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Several of the one thousand and one nights feature ruminants variably translated as deer, gazelle, hind, hart, calf, fawn, doe, stag, etc as you may well imagine, including the first of the three stories presented to the Jinni and thus framed within the frequently anthologized Tale of the Merchant and the Jinni.
A more important detail here is whether the cartoon itself was Australian...
Edited by NCF

I'm looking for either a film, or tv show that aired in Australia sometime in the 90s or early 2000s. I think it might have been part of a series of Arabian Nights stories but I'm not really sure. The bit I remember is a scene where this sultan or something is hunting a deer and and there is a little boy who's trying to protect the deer. I'm fairly sure the deer was magical...