AngularJS $timeout function not executing in my Jasmine specs

According to the Angular JS documentation for $timeout, you can use $timeout.flush() to synchronously flush the queue of deferred functions.

Try updating your test to this:

it('should do stuff', function() {
  expect($scope.stuffDone).toBeFalsy();
  $scope.doStuff();
  expect($scope.stuffDone).toBeFalsy();
  $timeout.flush();
  expect($scope.stuffDone).toBeTruthy();
});

Here is a plunker showing both your original test failing and the new test passing.