Does anyone know of any consulting firms recruiting entry level graduates (those with less than 2 yrs experience) in regions such as Dubai, Singapore, Malaysia etc

Most consulting firms in Dubai tend to recruit experience hires. I have not come across any that does entry level rec. Mercer have recently entered the market, it might be worth going to their website to find out. You can also try Mckinsey, BAH, Deloitte, EY, and KPMG.

I think you'd find that as far as Malaysia and Singapore are concerned, you'll need a work permit, very similar to the ones required by non EU residents who wish to work in the UK. I would think it would be easier to find such work in Dubai though, as the place is literally booming at the moment. Plus, the UAE is one of those countries which has a high percentage of foreigners in their workforce (I wouldnt be suprised if it was as high as 90 percent, if not higher), and as such, employers are less likely to baulk at the idea of work permits/sponsoring you. But you never really know until to give it a go really.

Jammy is right. There are no workpermit issues in Dubai, although you do need one but the company hiring you will have no problem in sponsoring you and getting the permit. You need to land the job from you home country and the company will take it over from there. I must add that the ideal expat packages in the Gluf/Middle East are on thier way out now, because its an employers market and people want to relocate to the middle east...