I have just returned to Qatar under exactly this circumstance.
My old employer gave me an open NOC which I could give to any company and then cancelled my RP.
I gave the NOC to my new employer who then had to contact my old employer to obtain the comuter card copy.
The computer card card copy and the NOC then went to immigration for them to grant me a new entry visa of the type which allows me to get RP again. This took about one week.
The only pain is that you have to go through the medical and finger print lark again.
I am just about finished with this procedure and I should have my new RP next week or so.
Hope this helps.

just eat another pie