When I got the rescue dachsies, Nutmeg, Cinnamon and Ginger in 1998, Cinnamon was really bad with the heartworms. The last day she was on this earth I rushed her to the vets, and I had to leave her there so they could do what they could for her (I was hoping she would get better). Later that evening Nutmeg was very restless, she was actually missing Cinnamon. I had to take her to the vet's office just so she could see Cinnamon. Once she saw Cinnamon she calmed down. Unfortunately Cinnamon didn't live through the night, the vet called at 5am to let us know Cinnamon had left us. Nutmeg actually went through a grieving period for quite a while.
Dogs do grieve, they have feelings. I remember the story of Greyfriars Bobby:
Story Of Greyfriars Bobby