By sponsoring an event like this, you will generally pay a fee for a table or space or tent (whichever that venue is offering).
Advertise for the other vendors on your social media!
Word travels fast in the pet-owner community.
Pet lovers consider pets to be part of their family (que in the word Fur Baby).
When you are attending these types of events and helping to find homes for abandoned pets is usually appreciated and you will get to meet and talk to new people.
Pet lovers bond with other pet lovers.
Some good marketing lines when you are sponsoring this type of event could be something like “Creating home for you and your pets”.