Jared, I absolutely love this idea. You have several approaches you could take with this. You could allow some of the profits you make to go to shelters for animals or to help with animal treatments. You could also ask if your customers want to donate as you mentioned in your post.
In addition to that, I would put in your about us section of your business on your website, why you stand for it. Why that cause matters to you so much and what you want to do about it. What kind of impact you want to make. Why your business helps fulfill two purposes. The goal and purpose of your business, but also how it aims to help animals and it’s a purpose in that.
A company that I advise on here, WPX hosting does something similar.