Short answer is it is not possible, and tasks must be recreated individually or using the Remote Management Services. There is no out of the box tool or solution to import or export tasks massively to be consumed in a different environment or server (i.e.: DEV to PROD).
Longer answer is that somehow, since mostly all that information can be found in XML files, you could eventually "copy & paste" the folder from the old server to the new one and have it working. You could also use the QMS API and read from the old server and create on the new one, even use third party products, if the workload is so big, like those NOADbi.com. I never used them so I cannot give you more insights.
If you have a spare server / sandbox or even a local server installation in your laptop, I would go for the copy & paste of the QVPR folder to the new server, changing the references from the old server to the new one and test that scenario.