Islamic art actually has lots and lots of representational art, both of people and animals. The restriction against representations is specifically related to religious art - so Qu'rans and objects intended for mosques. This is why there are lots and lots and lots and lots of representations.

Have a look at the Shah NaMeh of Shah Tamasp, for example, or the hundreds of texts that were translated and created in the House of Learning in Baghdad. These are covered in gorgeous, elaborate illuminations. Note that none of these were religious texts, and Qu'rans created in a similar time period are decorated with geometric illuminations instead. Similarly, there are metal and wooden objects covered in images of animals and people, such as bowls and candlesticks. If these objects were made for a mosque or have verses of the Qu'ran on them, then they have only geometric or floral patterns.

It seems to have become common knowledge that Islamic art doesn't have representational art, but this just isn't the case. Religious art isn't representational, but anything and everything else has decorations of anything under the sun (and sometimes outside of it - constellations!).

Have a look at the Aga Khan Museum's website for images of both secular and religious objects and art!