I'm not sure how well used such a park would be. However, if it is deemed necessary, the Euroa Showgrounds would be the obvious site; it's already fenced and used by many kinds of animals already, so it would require little if any modifications.
The creek walk is popular with locals and visitors, for its wildlife and its natural beauty. There are some areas that should be off-limits for dogs and cats. We are not all domestic animal lovers.