if you relocating to UAE, then surely it would mean you leaving Qatar?
which in turn means that your visa or right to be here is no longer valid ?

i have been told that once you leave qatar you cannot come back in to work for 2 years, likewise for UAE

maybe you mean that you are based here in Qatar and that you spend short period of contractual work in UAE?

let us know what answers you find as i suspect that many people will be looking to do this with the global recession in mind.
regards