Copy and paste Named Ranges

I copy a range of cells from a template sheet and paste them during
the creation of other sheets. The range is defined by a named range.

Public Sub InsStatRows()
'Insert Statistics Footer
Dim mySheet
Dim mySpace As Range

Set mySheet = ActiveSheet

Range("a1").End(xlDown).Offset(2, 0).Select

Set mySpace = Selection


ActiveSheet.Paste Destination:=ActiveSheet.Range(mySpace.Address)

End Sub

This works great but I also need to copy Named Ranges that are within
the source range. (some of the copied cells have names in them) Is it
possible to copy named ranges from one sheet to another? If yes,
suggestions please
These names are "local"