Answer: The answer is C)it's
Explanation: If you read the sentence, it makes sense and it is not exactly explaining a gender. The dog stretched it's limbs, yawned loudly, and then began to look for it's bowl.
It would not make sense if it was The dog stretched their limbs. Their is for more than one person or another person, as in a possession. It would make sense to use their if there was more than one dog. The dogs stretched their limbs.