I'm an animal lover, and I wouldn't do it. My very friendly, older, well cared for Golden Retriever has caused numerous damages to apartments (and now our house) when an unexpected thunderstorm came up, or a neighbor's fire alarm was going off all day, etc. We were responsible and paid to replace the carpet, paint the front door, etc., but I would not do it. You wouldn't know my dog was schizo from meeting her.
My cat, who is also well cared for, inside only, started peeing in a corner of our rental dining room, despite having a clean litter pan, because he had an infection we didn't know about. It was several days before we realized what was happening, and the damage was done.
In this area there are so few rental places available that I'd think you'd have no trouble finding a tenant. If you do, then maybe you could reconsider. Having been a tenant, I was grateful for being able to find places that would lease to us as pet owners, but if I was leasing my own place out, I wouldn't! Double standards, I guess.