VISA & NOC

Hello good morning! I just wanted to have a clear and correct answer regarding about my problem. I came here having a family visit visa (Father Sponsor), Then after a few months, I was employed to a private company and was transferred to their sponsorship as what the company told me. The company issued me a working visa for 5 years and it's already on my passport but, there's a STAY EXPIRY for only 3 months. They haven't sent me yet for MEDICAL or FINGER PRINTS. I only worked at their company for only 1 month due to some problems & I don't want to continue working with them. And now, I want to find another job here in Qatar.
-Should I need to acquire an NOC from the previous company so that I can be employed to another company?
-Do i have to exit here in Qatar and apply for new Visa (i.e family visit visa )?
-What are the possible Visa type can I apply for re-entry?
How long can I re-entry here in Qatar after my exit period? I need your advice guys. Thanks in advance.