Having just recently changed companies myself, I am able to say, that until the "original" copy of the NOC is in the possession of the new sponsors, there is legal obstacles in having you work with the new company. Unless the new company is able to provide an "original" NOC the sponsorship will not be legally recognised by the Qatar government, and therefore, one cannot legally perform for a new "sponsor"/employer. Remember ORIGINAL NOC only is recognised not copies, by all means make a copy for your own purpose, but make sure the original is sent to the new employer, or better still take and deliver it to the HR dept of your new company where it will be kept on file. They will require it for change of residency purposes, also..
Having just recently changed companies myself, I am able to say, that until the "original" copy of the NOC is in the possession of the new sponsors, there is legal obstacles in having you work with the new company. Unless the new company is able to provide an "original" NOC the sponsorship will not be legally recognised by the Qatar government, and therefore, one cannot legally perform for a new "sponsor"/employer. Remember ORIGINAL NOC only is recognised not copies, by all means make a copy for your own purpose, but make sure the original is sent to the new employer, or better still take and deliver it to the HR dept of your new company where it will be kept on file. They will require it for change of residency purposes, also..