You need to cancel your visa from the current company and I doubt if they will do it because they have to provide an amount equivalent to one (1) way ticket at the airport immigration. If this is not possible, wait for six months, the visa will automatically be cancelled.

My advise, come to Qatar and work with them. Resign after days, weeks of after a month. Return with the new sponsor's visa. So far this is the easiest and less complicated process.