If your relative or friend already working in Qatar, you can ask for a reference. Mostly the common practice is if the company having a job opening, they ask first to their staff if they know any suitable candidate. Because they can save some time and advertisement expenses like that way.
2) Job Portals
Explore your search skills, You can look for available vacancies on popular career portals like qatarliving.com, indeed gulf and qatarjobfinder.com, etc. A good company will not charge anything to hire you, they will spend on visa, travel expenses and medical for you.
Most of the companies try to find the candidate through Job portals before they look for any job consultancies. You have to create an attractive resume mentioning your desired job profiles and work experience in detail. If the company finds you suitable for the job, they will contact you directly.
3) Visit Qatar and search directly:
Now Nationals of more than 80 countries are eligible for visa-free entry to Qatar, and they can stay in Qatar from 30 -180 days depends on the country. you can find more details here
If you can afford you can plan your visit to Qatar, and go to companies directly and drop your Resume. If you are lucky and enough qualifications, you may get your dream job immediately.
Things to take care of
Before agreeing to an offer, be aware of scams related to fake jobs. Investigate the Company, find the nature of its business and the condition of their employees. Talk with the Company regarding your salary, benefits and the legal terms before signing the contract.