I'm not sure if this has already been posted, but I am afraid that all the dogs on the voyage were also shot, and buried. You will have to read the book to understand the situation. Although I am against senseless killing, I completely agree with his decision.

The crew had to abandon the ship and tow the three boats across the ice. There was a danger that at anytime the ice could split up underneath them, sending people and equipment in different directions and into the water. The crew had to be completely ready to abandon the flow and board the boats, something that would have been made much harder, had there been animals present.

It was not as if they had happily shot the animals and carried on, as before with all their comforts. They had all been forced to abandon any equipment not absolutely necessary including all their photos of family and a lot of the food of lesser value. The extra mouths also meant less food per person and extra water would have to be melted for the animals to drink. The crews blubber supplies were very low and they were often forced to eat snow for water.

I hope this sheds some light on the situation.