I doubt Yurovsky and his men would have gone to the same lengths to dispose of a small dog's body as they did with the humans. It seems to me that just dropping the dead dog somewhere out in the forest for the wolves and other carrion eaters to dispose of would have sufficed. People would have been looking for the Emperor, not a little dog...
If I took a guess, I'd say the dog's body would have been taken off the truck the same time as the others were the first time and no one bothered to pick the dog's body up and the men and the human bodies in the carts went off to the Four Brother's Mine.
See THE FALL OF THE ROMANOVS by Steinberg and Khrustalev pps. 351-356 which has Yurovsky's 1920 statement:
>>>>Around 3 o'clock in the morning, we departed for the place tha Ye-v was to have prepared (beyond the Upper Isetsk factory). First it was assumed that they [the corpses] would be brought by car and then, beginning at a certain point, on horseback, since the car could go no further. The place selected was an abandoned mine. After driving a little more than 3 miles past the Upper Isetk factory, we bumped into a whole encampment -- about 25 people-- on horseback, in light, horse-drawn carts, etc. There were workers (members of the soviet, of the Executive Committee, etc.) whom Ye-v had prepared. The first thing they exclaimed was: "Why didn't you bring them to us alive?!" they thought the Romanovs' execution would be entrusted to them. They began to load the corpses into the light carts, but wagons were needed. This was very inconvenient. They immediately began to clean out [the corpses'] pockets -- it was necessary to theaten them with being shot and to post sentries here as well. Then it was discovered that Tatiana, Olga and Anastasia were dressed in some kind of special corsets. It was decided to strip the corses bare, but not here, only at the place of burial. But it turned out that no one knew where the mine was that had been selected for this purpose. <<
AGRBear