Business Visit Visa to Work Visa

Hi All,
I am here on Business Visa through one of the company with whom I am working. I am here since June 2012 so every third month this company sending me and calling me back in Qatar on same business visa.
Last month I was selected in a good company with my expected salary, so they have sent me offer letter and i have confirmed offer on mail.
Now my Question is where I am selected they are asking NOC from my current employer (Sponsor), While I requested NOC from my current employer they told on business visa you are not required NOC means we will provide you exit permit and experience certificate you can exit from qatar and you next employer directly apply your work visa. So is it true? because where I am selected they have not call me for contract signing as I passed same message to them what my current employer saying to me.
I can go beck and the next employer will directly apply my Work Visa! is it?
And whenever I am calling them they are telling me that your contract is under process so is it true that it is taking too much time for person who needs new work visa?
Can you provide me information how they will start my visa procedure?