Department changing

How can I change my department from Production- packing to QA?

Its depend upon compony policies.

Firstly please make up your mind to change the department. Study QA aspects thoroughly before you switch to QA from production. Your experience in production would be definitely helpful in QA, however, you will be considered as fresher for at least a few months untill you gain good knowledge and experience on your new job responsibilities / assignments.
Talk to your immediate supervisor and decide further steps.