Sorry to hear. We don't take dogs but have had some occasional really bad carpet stains.
1) Recommend always having a relationship with a professional cleaning firm beyond your normal cleaner/steam cleaner. They are pros in cleaning all sorts of damage. They can recommend and quote on what to do.
2) Photo and quote and get it into airbnb asap for a claim. The guests need to pay for this. Be professional and courteous to guests understanding the dog situation but they need to responsible for what happened.
3) You may also be able to claim on your own insurance for loss of income given you had to cancel.
4) Do a review on the guests on the 14th day being factual on the cleanliness and that the dog caused issues. It's not your fault that it just happened in your property even if its not normal for the dog. It's the risk that dog owners take when travelling with them.
5) I'm hoping you didn't get penalised by airbnb for cancelling a booking?
All the best, hopefully you can get back on track quickly and be compensated for most of the remediation. Unfortunately its just bad luck, and sometimes that happens hosting. The cost of doing business....
Regs MK