You cannot get a driving licence on a visit visa.
Even if ur on an employment visa, there are specific professions which are allowed to obtain driving licence e.g. Doctors, engineers, business men etc.
Dubai is no longer a heaven for us asian expats. Those who came in the eighties made a lot of money. Now its tough but still.... if you have the will and faith... anything is possible.
On the whole, situation in the job market is bad. Lots of businesses have shut down or downsized to reduce overheads.
Still i'd say there's no harm in trying. Do ur best, leave the rest to the creator