Have you considered getting another pet? Many times caring for something is what keeps people going. Whenever I get screwed up I pick up one of my cats and it helps.
Also if you have been depressed for a month now it could be more than just the death of your dog. It is possible that this episode of depression is independent of the pet.
I got really really depressed after a relationship ended when I was 18 and attempted suicide. It turned out that it wasn't the relationship ending that made me depressed but chemical factors in my brain caused by a physical injury.
I'll give you the same advice that I should probably take myself: see a psychiatrist and ask if this is depression. If so you can get medicated.