Also this is the current sponsor's choice, you can kindly request him to let you transfer directly, but he has the final say. Best is, to get new sponsor to atleast have approved visa of your nationality available, so soon as you exit, new sponsor can apply for your visa,... it will take 3 days if new company PRO is not lazy. So practically, you can be back in Qatar in 3 -4 days. Consider it as paid vacation, as old sponsor should pay for your exit ticket, and new sponsor should pay for your entry ticket to Qatar :)

Hope this info helps.