I think for the first change in sponsorship one has to finish minimum 2 years of job, for second change onwards it is 1 year.
You have to locate a new company, who are willing to take you on job under their sponsorship, get your Police clearance attested from the Ministry of Interiors (C ring road), then give the papers to PRO to fill the transfer form, get it stamped by immigration, authenticating the CR number, take it to your old company, they would do the same and return it back to you, hand over the papers with your ID card to the new company PRO and he would do the rest, after change a new id card would be issued and it is done!! if you are changing to a ovt job, you need medical done again and you need a police clearance from qatar Govt too (from Salwa road office after fort r/a)