Kimberly, I applaud you for your statement. This is a topic that I believe will touch the heartstrings of the reviewer since animal rights and causes are close to the hearts of everyone in the country. The mere topic of saving animals, albeit a dog in this case, shows that you are a person with a kind heart who does not take kindly to the maltreatment of the helpless. As a student, this shows that you will be an asset to their university because of your kind heart and close affiliation to a cause.
Now, when you discuss the part about changing the lives of a small few, I suggest that you continue the discussion by mentioning either the activities that you participated in at the shelter, or the programs that you helped them start. Don't bother with discussing how you hope the university can help you further your cause. That is not something required in the prompt. Your concentration should be on recreating your character on paper, as the prompt requires. So expand on the discussion about saving animals and how you participated in it. The reviewer will be able to put two and two together as to how that will translate into the kind of student that you will be at their university.