There is two way to automatically send a call to a post call survey once the agent is done. But this is not support in UCCX directly. You can use Cisco CVP 3.1 or above the post call survey feature is build in. If you’re using IP gateway, you could also setup a TCL script on the inbound IOS Voice Gateway that transfer the call to an IVR as a second step.

However the best way is go with a custom “disconnect” button that actually triggers a call transfer to your route point. You can configure a task button to transfer the call to the secondary app. What nice about this solution, I found that in the database the SessionID associated with the initial call, and the SessionID associated with the second call being transferred to the Survey application were the same.
This meant that we could write a custom report that told them how many calls each agent had taken, positive/negative responses received, and how many calls had been transferred to the survey. This allows the Supervisors to see each agent’s performance, and identify people who are avoiding the survey.
 

Could you please share the script you have for the data collection.  I have been looking into this as well just haven't had the time.