@Jayne212
According to Airbnb, Aircover (the new replacement for Host Guarantee) now includes pet damage. See: https://www.airbnb.co.uk/resources/hosting-homes/a/introducing-aircover-469
I am really not sure whether you would have success or not as hosts' experiences of filing a claim for damages seem to be varied. I've only claimed once and found it really easy and straightforward, but that is not everyone's experience.
Make sure you take photos/videos of the damage and also keep any correspondence about it with the guests on the Airbnb messaging system. You will also probably be asked to provide a quote/invoice for fixing the damage and receipts for broken items or proof of the cost of replacement ones.
Consider also the review. As guests can sometimes respond to being asked about damage with a revenge review, which is normally very hard to get removed, consider waiting until just before the 14 day deadline to post yours, so as not to prompt the guest to leave a review. Unless, of cousre, the guest goes ahead and writes their review before that...