Providing you are allowed in, I wouldn't bother with the shopping. If you go to one of the Malls you could be anywhere in the world. Next is the same as Next anywhere, except it is more expensive in Dubai. Chanel is the same as Chanel in London and New York, except it is more expensive in Dubai.
If you want knock off goods, head to Karama, where the quality of the handbags is good but don't come at Asda prices as the nice man will lead you to believe. Don't forget they are genuine fakes that you are buying.
You could get a taxi to the Sheraton Dubai Creek and walk back along the Creek and watch the boats being loaded and unloaded. You will be transported back in time by 100 years. You will see drums of oil stacked beside sacks of rice and all being loaded on and off the boats by men in flip flops and not a High Viz jacket in sight. If you are really lucky you will see a little man knocking a curry up in a pan lid on a boat and on the next boat there will be another man with his bare bottom sticking out through a make shift toilet seat getting shot of last nights curry. He may even give you a wave. I got one.
Take a ride over the Creek on a dodgy boat, I think it costs aed1 or something like that and head for a riverside cafe. If you are a women you would be hustled out and taken upstairs to sit on plastic chairs with a lovely view over the Creek. The food will be very cheap and very good. Ours was served by a dwarf. I don't know if I should say dwarf, it isn't PC, but that is what he was.
Alternatively you could do a Dubai Big Bus tour. Don't laugh, I'm serious. I haven't done it myself but my dad did. He didn't get off the bus even though you can hop on and off, but please wait till the bus stops first.
If you aren't familiar with Dubai the bus will show you all the sites and give you a guided tour. Mint!
When you get back to the airport head to the Irish Bar which isn't very Irish but sells alcohol and have a couple of drinks while you wait for your next plane.
Enjoy!