There are probably common folktale variants on Liu An’s dogs ascending to heaven. But it’s a good fit with Daoism since so many strains of Daoism stress configuring oneself with the given. Liu An’s dogs (and Liu An himself, for that matter) act or “way-make” appropriately given the environment in which they find themselves.
More exactly, the dogs respond appropriately to shi, Chinese for propensity, configuration, or set-up. In The Propensity of Things: Toward a History of Efficacy in China, François Jullien unpacks this concept at length. (A book I found thanks to my friend, Miles, who introduced me to the Kinokuniya Bookstore in San Francisco.)