Switching HDs isn't recommended as those MBPs aren't identical thus have different drivers which might cause issues.
If you want to use your current HD, use Migration Assistant to transfer your files to the new Mac, then put the HD from your old Mac to an external enclosure (Target Disk Mode could also work) and wipe it with Disk Utility and then clone your internal HD with Carbon Copy Cloner and then just swap the HDs and you're done
Don't hesitate to ask, it sounds complicated but it isn't