You should be able to be out by 8:00 and the ride to Sharjah should be fast - most the traffic is going the other way. I could get from Jumeirah to Sharjah in 45 minutes. DXB is usually not too crowded that early, so it should be ok - I have never used EK's service but a regular tax should be able to do it.
Have you flown Air Arabia? Where are you going? They're a great airline.