Funnily enough you can't duplicate a folder which contains Google Documents

Duplicate a template folder in Google Drive using Google Apps Script

function duplicateRootFolder() {
  var templateFolder = DriveApp.getFolderById('PUT YOUR TEMPLATE FOLDER ID HERE (FROM YOUR BROWSER URL)');
  var targetParent = DriveApp.getFolderById('PUT YOU PARENT FOLDER ID HERE (FROM YOUR BROWSER URL)');

  duplicateFolder(templateFolder, targetParent, false);  
}


function duplicateFolder(templateFolder, targetParent, useTemplateName) {
  var newFolderName = templateFolder.getName();
 
  if (!useTemplateName) {
    var dt = new Date();
    var dtstring = dt.getFullYear()
       + '-' + pad(dt.getMonth() + 1, 2);
    var newFolderName = dtstring + '-0000____ PENDING DUPLICATE';
  }  
  var newFolder = targetParent.createFolder(newFolderName);
  
  // we copy all files
  var files = templateFolder.getFiles();
  while (files.hasNext()) {
    var file = files.next();
    Logger.log(file.getName());
    
    file.makeCopy(file.getName(), newFolder);
  }
  
  var subTemplateFolders = templateFolder.getFolders();
  while (subTemplateFolders.hasNext()) {
    var subTemplateFolder = subTemplateFolders.next();
    Logger.log(subTemplateFolder.getName());
    
    duplicateFolder(subTemplateFolder, newFolder, true);
  }
}

function pad(number, length) {
    var str = '' + number;
    while (str.length < length) {
        str = '0' + str;
    }
    return str;
}