To confirm the inference that different dog breeds are classified as the same species, the most critical piece of information you'd need is similarities in DNA.
While similarities in diet, color, and behavior might provide some insight into the relationships among the breeds, they are not definitive indicators of species classification. DNA analysis can reveal genetic similarities and differences that are essential for establishing whether two breeds belong to the same species. In the case of dog breeds, they all belong to the same species, Canis lupus familiaris, and genetic studies confirm their shared lineage.
Thus, while other factors can support the idea of classification within the same species, genetic data is the most reliable and scientific basis for such determinations.