For appropriately Arab dress, those fashions are perfectly fine. However, the tale itself purports to take place in Tang or Song Dynasty China, while the names of its main characters suggest Khwarzim-era Persia, immediately prior to the war with the Mongols. (Aladdin is the name of the last Khwarzim Emperor, and his father in law shares his name with the Khwarzim Emperor who provoked the Mongol invasion of the place,) As setting it in the former might become the root of a diplomatic incident in the wake of Tiananmen Square, I suspect the dress fashions would have to change subtly to match the setting of the latter, if we're going for absolute authenticity.