Procedure for Visa transfer
1) Get NOC letter, CR copy, Computer card copy from the current sponsor. If you dont have NOC forget about everything, whether you are locally hired or globally hired, under current rules.
2) Current sponsor fills the visa transfer application form (form requires new sponsor company name, computer card no, telephone no to be filled) and perform sign verification at the emigration and give to you.
3) Take that to new company who do the same verification at the emigration and give that to you along with reference letter to CEID (CEID verification may not be needed for private companies)
4) Take your country's PCC at your embassy (2 days for Indian PCC)
5) Take these to CEID at Salwa road (to repeat, this may not be required for private companies) and submit form for Qatar PCC filled (given by them), along with original India PCC, copy of visa transfer application, copy of NOC, copy of ID, copy of Qatar attested educational certificate. They may require you to take fingerprint in the same building. Also take originals of these in case they ask, even though they didnt for me.
6) Give the receipt to the new company (keep a copy for yourself) who will follow up.
7) When Qatar PCC is obtained (informed by Metrash also, takes 2-5 days) the new sponsor collects it and submit the original visa application, original Passport, original NOC and ID, old and new company CR and computer card copies along with the PCC and Attested Degree certificate copy to the labour for sponsorship change approval.
8) When the labour approval is obtained (9 working days for me), which can be checked online if you have the application number, the new sponsor goes to the emigration and obtain the new ID by paying the transfership fees.
You may note that the degree certificate should be attested by Qatar embassy in your country and then at MOFA at Qatar. Agencies may take 2 weeks to 1 month for completing the attestation. So if you want it fast you may have to catch a flight yourself. Also I heard now MOFA is demanding reference letter from the institution where the degree was granted for attestation for some countries. Also this certificate has to be translated to Arabic and authenticated by some approved typing center.
Also note that there are uncertainties involved like chances of rejection at various stages like CEID verification, labour approval etc even though they are supposed to be rare.
So plan in advance.