As a dog owner, I think we need to make sure we keep ourselves grounded from time to time and stop thinking about them as children who should some day bury us (or dig us up, depending on the dog and their love of digging).
Dogs are lucky in that we can say "It's time" and they can go in a painless, peaceful manner. How many of us would prefer that our loved one could tell our doctor the same thing, should we find ourselves in a terminal situation? Put yourself in their paws: would you prefer prolonging the inevitable or to go out while you still have the ability to say "Goodbye".
I don't think that many living creatures fear death as much as they fear the loneliness caused by the absence of those we love. I don't fret my own death but I'm saddened by the loss of time I'll have with my son and family. I'm not afraid of my dog dying, I'm afraid of how my life will be less joyful when she's gone.
You may believe your dog to go on to "Doggy Heaven" or that great Indian "Happy Hunting Ground". My belief is that nature is too efficient to not recycle life. So think about your dog not as ending, but as having a chance to begin again. Even though I'm an agnostic, I have a feeling that life happens more than once and sometimes if someone is really good in life and really does something the karmically prove themselves worthy of a reward, that being gets to come back in their next form as a dog. I can't imagine much better than the life of a dog that's loved and brought into a family as a member, not just a pet.