Yes, Qatar based companies do recruit from time to time but its best to secure a job from Nigeria, infact 70% of people in Qatar came here from their respective countries to find a job and you are no exception, but first, if this is your first time of working abroad, it is adviceable to be prepared before you leave Nigeria to work outside so you do not find yourself in a desperate situation that might force you to pick on 'anything' when you get here.
Theres no qatar embassy in Nigeria at present.
Just check online at the website dpatrick sent you for jobs matching your qualifications and experience.Also try this link http://www.gulf-times.com/site/topics/index.asp?cu_no=2&lng=1&template_i...

There are jobs but it doesnt come on a golden platter, just as in every where else in the world.But if you get a job, they will surely make you a work visa.

Wish you luck too.