Google-sheets – Entire sheet as a function

1. You don't want to filter the whole column if you need subtotals somewhere below the data. If you filtered the whole column, the subtotal row would be filtered out. So, to filter the data for April:

   1. Select your data table
   2. Data > Filter
   3. Small arrow by the header of the needed column > Filter by condition... > Custom formula is > enter this formula: =month(A2)=4 > then OK
      
      (My dates are in column A)

2. For subtotals just use the formula below your data like this: =subtotal(9,D2:D7)

3. In a separate sheet I would use a formula which is not dependent on the filter, like this:
   =sum(arrayformula(Sheet1!D2:D7*(month(Sheet1!A2:A7)=4)))
   If your sheet name consists of several words use commas when referencing it like this:
   'My data'!A2:A7

This can be done with a script, using insertSheet method which takes the new sheet name and the template after which it's to be created. The first function adds a custom menu item when the spreadsheet is opened, the second performs duplication when that menu item is invoked.

As far as I can tell, the contents are copied over in the same way as they are with "Duplicate" function.

function onOpen() {
  var menu = [{name: "Duplicate and name", functionName: "dupName"}];
  SpreadsheetApp.getActiveSpreadsheet().addMenu("Custom", menu);
}

function dupName() {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = ss.getActiveSheet();
  var name = Browser.inputBox('Enter new sheet name');
  ss.insertSheet(name, {template: sheet});
}