Oh! I'm so sorry about your dog. That is a very hard things to have to do, and it is like losing a family member. It's good that you got to say goodbye to Barney, I'm sure he appreciated your being there, too. Your little Winnie is no more a replacement of Barney than Barney would be for your grandmother, that's not the way it works. I hope, though, that you will cherish Winnie just as much.
Thanks for posting this, some people don't realize how hard it is losing a pet.