I never really experienced any major traffic problems during my 8 day stay in Dubai back in March to be honest. For a city of its size, the traffic seemed manageable, although we did get caught in jams a couple of times at rush hour (but nothing that took more than 15 mins to clear).
That said, the city is really spread out... JBR, downtown, Deira/creek, and Jumeirah are really all like separate cities connected by major highways. If you're staying out by the airport, which is where we stayed (at the Raffles Dubai - best hotel I've ever stayed at), then you should be no more than 45 minutes from Downtown even if there's major traffic issues enroute. Mall of the Emirates is smack dab in the heart of downtown.
If you're able to stay within walking distance of the Metro, then you can easily use it to access almost all major attractions (including Mall of the Emirates) in 30-40 mins from the airport area, because the one and only metro line runs along Sheikh Zayed Rd all the way out past JBR. Obviously that doesn't help you get out to the desert in any way, but it does mean you have a reliable means of getting downtown to the Mall / Khalifa even if traffic sucks.
For what its worth, during my entire stay in the UAE, our desert safari excursion was by far the most enjoyable and memorable thing we did. That shit is some SERIOUS desert. I'd recommend Platinum Heritage Tours if you decide to go on a quality desert tour (they have an afternoon/evening tour that begins in mid-afternoon and ends around 11pm, including driving time to and from our airport-area hotel). I posted some pics of the tour in
this thread.
Good luck chief.