I do specify what kinds of pets are accepted (dogs and cats only, no known bite/attack/aggression history, proof of vaccination, etc.).

 - She is offering to pay more pet fee (I am already charging $200 upfront and $25 additional every month)- The house is old (1952), has hardwood floors, a new deck, and a large backyard- The tenant is required to get renter's insurance- I have asked her to provide a record of the dog being spayed/neutered as well as vaccine recordsIt may or may not be obvious that I would like to approve this tenant even with the dog.  

Asking to be provided proof of recent vaccinations of the pet will also help ensure you have a responsible pet owner.And as @Steve Vaughan stated above, small dogs tend to do the most physical damage.

They gave me a pet deposit, but I subsequently found out when a possum came in the house that the dog wasn't vaccinated for rabies.

Unfortunately, many of these doctors offer their services on line to provide this certificate with letter for a fee.You can accept the animal under reasonable conditions, such as require that the animal be registered and that the tenant show proof of current vaccination and that the animal is not an aggressive threat to others. 

If you prefer to let your cat out, it has to be supervised and leashed.Dogs : We allow adult well trained and well cared for dogs, they should be vaccinated up to date, clean “bite record from the vet” is required.

If you prefer to let your cat out, it has to be supervised and leashed.Dogs : We allow adult well trained and well cared for dogs, they should be vaccinated up to date, clean “bite record from the vet” is required.

I simply told my tenant that if she can provide a legal prescription from a licensed physician, she can have the dog but must provide proof of all vaccinations as they become due from a licensed veterinarian.

However, you can request to see proof of current vaccinations, alteration certificates, training certification as well as a third party letter from a licensed professional stating need for the animal and why.

No one is curing COVID-19 any time soon, and even if that vaccine came out tomorrow it will take a long time to administer it to hundreds of millions of people.Overall rate trend CONTINUES slowly downward, in spite of this little blip.