Since you are in unlimited contract, submit resignation and work one month for your notice period, collect all your dues cancel your residence visa and exit Qatar.

Ask your new employer to apply your visa while you are out of country and come back to Qatar once your visa is approved.

NOC is required only if you want to transfer your visa without cancellation.

Ensure you have new company offer letter and full support from your new sponsor company PRO before taking any actions.

Also check whether they have your nationality & designation visa and they are ready use/apply for you once you exit the country.