To be blunt - you can think and hope all you like @Jaklin--Aka--Jacqueline-0 but the chances of this happening are pretty slim - hosts have been asking for this feature for years and it has fallen on deaf ears.
The best you can do is state in your house rules you charge extra for pets. There is also a section under pricing - right down the bottom - "standard fees and charges" "other standard fees" where you can opt to charge for pets. A word of warning however - from the guest perspective this will be buried right down the bottom of your listing in house rules and is not very obvious - it will also not show up in the total price when they are searching, but will be an "added on" cost - potential for disgruntled guests - so if you're going to do it, be very clear about it in your listing. I'd also make sure you mention it again when guests have just booked ( if you have IB) or are requesting to book...
@Jaklin--Aka--Jacqueline-0 I wouldn't offer a refundable deposit if the dog turns out to indeed be housebroken or doesn't cause damage. It would be like offering a refundable cleaning deposit if the place is left clean. It opens to door to dispute- what someone else might consider to be clean might not be yours, or a guest could claim that the urine smell on the carpet must have been done by some previous guest's pet, certainly not their little darling.
You can always send the guest an unexpected "surprise" refund if they are extraordinarily respectful, if you feel it's warranted.
