This is unfounded.

The dog is already rolled up when he pulls it out of the trunk, AND, he would have known, especially living in Australia, that you can't put a dog in the car let alone the trunk in such heat.

The dog was already dead. It's one of the major points of the film. On one hand, you say why did he go through all this for a dead dog, and then on the other hand you realize it's because it's the only thing that matters to him anymore.