Qatar is diversifying, visit Qatar and you will know
Doha is coming as competition to Dubai, gaining as another financial hub in this region. Right now many people I know are relocating from here (Dubai) to Doha since job opportunities are better there at the moment. It is growing much faster, expected GDP growth for 2009 is 12%, while UAE's GDP growth for 2009 is expected to be only 2.5%
Dubai doesn't have much oil anyway so comparison is useless for the oil. If Dubai had oil then still it would have made at least 60% of the exports. But in terms of growth in non-oil sectors Doha has taken the lead in the region.