@Cheri38 Accepting dogs works really well for us: a lot of our guests bring them along. I would say it's boosted our occupancy rate quite a bit. In 2 years of hosting, I've only ever had one dog that was a pain and I wouldn't host again: most of them are great. If it would make you feel more secure about it, maybe put in restrictions like only dogs under a certain weight are allowed, or dogs have to be crated if they're left alone. We also provide paw towels and old sheets to cover furniture if the weather is messy, which helps.
However, it's important to note that the Airbnb "security deposit" isn't a security deposit, it's just an amount they could be charged if there is damage. Airbnb has to agree with you that there is damage that needs to be covered by the guest, or the guest has to agree to cover the damage. Pet damage isn't covered by the host guarantee either.