@Joey210 Airbnb does not charge or remit deposits on hosts' behalf. If you'd like to run a deposit through the platform, Airbnb is not the right choice for your listing. In the event that your property is damaged, the process for compensation is unwieldy, often unsuccessful, and completely at the mercy of the case manager who receives your documentation. This process has nothing to do with your deposit, one way or other.
The "Host Guarantee" does not cover damage caused by pets, so if this happens and Airbnb isn't able to collect a further payment from the guest, you're out of luck.
Anyway, given how sensitive an Airbnb listing is to reviews, a refundable deposit is a poor choice; if there is any reason not to refund the full amount at the end of the stay, you're guaranteed a retaliatory rating that could sink a relatively new listing. Far easier for you would be a non-refundable pet fee - disclosed on the listing, payable as an "extra service" after the booking is confirmed via the Resolutions tool. This allows you to get the pets "registered" before the stay, so the thorny topic of money doesn't have to be addressed again.
Enter whatever amount you want as a security deposit; it doesn't matter, because it won't be charged anyway.