I think it best that you talk to someone in Qatari immigration for the most accurate answer as most likely no one answering your question is an immigrations expert. For what it is worth, my understanding is that as long as you fulfilled the terms of your original contract, which it sounds like you did, then there is no requirement for NOC or a time ban should you wish to return to Qatar with a different employer. This is of course assuming that you left your former employer on good terms. You completed your contract, chose not to renew your contract and have left Qatar - correct?
I think it best that you talk to someone in Qatari immigration for the most accurate answer as most likely no one answering your question is an immigrations expert. For what it is worth, my understanding is that as long as you fulfilled the terms of your original contract, which it sounds like you did, then there is no requirement for NOC or a time ban should you wish to return to Qatar with a different employer. This is of course assuming that you left your former employer on good terms. You completed your contract, chose not to renew your contract and have left Qatar - correct?