@Darius1, in your shoes, I would contact AirBnB to report the damage and find out whether it's possible to recoup damage costs via the resolution center.
Here's a thread with the Resolution Center link.
Be sure to take photos to show the damage.
For the future, I'd suggest you request a Security Deposit and beef up House Rules. They're generic at the moment, and leave you open to all kinds of unfortunate occurrences. For instance, one of the rules should be that if damage occurs, guests are to inform you immediately so that the appropriate steps can be taken. You might also want to reconsider allowing guests to bring animals.
You might also make a point of taking photos of every area of your accommodation that guests would be in. That way, you can check afterwards to make sure nothing is broken, damaged, or missing, especially because any claims against a Security Deposit need to be made within 48 hours of a guest's departure. The photos thing sounds over-the-top, I know, but I've learned a lot from the stories told by other members here.
I hope other, more experienced hosts, will chime in here with suggestions.