Based on Irvin Dominin example, I've created 2 examples supporting Paste and hit Enter.
This works in Chrome:
http://jsfiddle.net/lhernand/0a8woLev/
$(document).ready(function() {
   $('#date-daily').datepicker({
      format: 'dd/mm/yyyy',
      assumeNearbyYear: true,
      autoclose: true,
      orientation: 'bottom right',
      todayHighlight: true,
      keyboardNavigation: false
    })
    /* On 'paste' -> loses focus, hide calendar and trigger 'change' */
    .on('paste', function(e) {
      $(this).blur();
      $('#date-daily').datepicker('hide');
    })
    /* On 'enter' keypress -> loses focus and trigger 'change' */
    .on('keydown', function(e) {
      if (e.which === 13) {
         console.log('enter');
         $(this).blur();
      }
    })
    .change(function(e) {
      console.log('change');
      $('#stdout').append($('#date-daily').val() + ' change\n');
    });
});
But not in IE, so I created another example for IE11:
https://jsbin.com/timarum/14/edit?html,js,console,output
$(document).ready(function() {
   $('#date-daily').datepicker({
      format: 'dd/mm/yyyy',
      assumeNearbyYear: true,
      autoclose: true,
      orientation: 'bottom right',
      todayHighlight: true,
      keyboardNavigation: false
    })
    // OnEnter -> lose focus
    .on('keydown', function(e) {
         if (e.which === 13){ 
           $(this).blur();
         }
    })
    // onPaste -> hide and lose focus
    .on('keyup', function(e) {
         if (e.which === 86){ 
            $(this).blur();
            $(this).datepicker('hide');
          }
    })
    .change(function(e) {
       $('#stdout').append($('#date-daily').val() + ' change\n');
    });
});
If last example still doesn't work in IE11, you can try splitting the setup:
// DatePicker setup
$('.datepicker').datepicker({
    format: 'dd/mm/yyyy',
    assumeNearbyYear: true,      /* manually-entered dates with two-digit years, such as '5/1/15', will be parsed as '2015', not '15' */
    autoclose: true,             /* close the datepicker immediately when a date is selected */
    orientation: 'bottom rigth',
    todayHighlight: true,        /* today appears with a blue box */
    keyboardNavigation: false    /* select date only onClick. when true, is too difficult free typing  */
}); 
And the event handlers: (note I'm not using $('.datepicker').datepicker({)
   // Smoker DataPicker behaviour
    $('#inputStoppedDate')
    // OnEnter -> lose focus
    .on('keydown', function (e) {
        if (e.which === 13){ 
            $(this).blur();
        }
    })
    // onPaste -> hide and lose focus
    .on('keyup', function (e) {
        if (e.which === 86){ 
            $(this).blur();
            $(this).datepicker('hide');
        }
    })
    .change(function (e) {
        // do saomething
    });