Simple answer: "essen" (to be) doesn't affect the case of the predicate, so "Das ist ein Hund" is correct. More thorough answer: If the verb requires the accusative case (the direct object of a transitive verb), then the masculine article declines to "den" or "einen," such as in "Ich habe einen Hund" or "Ich möchte einen Hund." If the verb is intransitive, the masculine article is normally in the dative case "dem" or "einem", such as "Ich gebe dem (einem) Hund das (ein) Spielzeug." In the case of the verb "essen" (to be), it is a copular verb and so it doesn't affect the case of the predicate; it remains in the nominative case: "Das ist ein Hund." Think of it as a math equation: "this equals that" or "that equals this."
Grammatically speaking for English, noone would ever say "these are a ...". It would often either be "this/that is a dog and a cat" or "those are dogs and cats". If you're going to say "these" then the more correct way to say it would be "these are dogs and cats" because "these" is plural but "a + singular noun" is singular.
In English you have a choice between this/that is and these/those are. You cannot mix this/that with are and these/those with is. Having said that, you can say these/those are a cat and a dog. It is grammatically correct, but less natural, less idiomatic, than that is a cat and a dog. English does not allow the equivalent of das sind or ce sont.
While I understand the grammar involved and I translated it this way, it would be very odd to hear someone in the United States say "these are a dog and a cat." It would be far more likely to hear a singular article and verb, however ungrammatical that might be. "It's a dog and a cat" "that's a dog and a cat" "this is a dog and a cat." Even in answer to the question, "What are these?" you would be more likely to hear "It's a dog and a cat" than "these are a dog and a cat." I can think of scenarios where one MIGHT answer "these are" but they're very rare (such as a German asking "Was sind das?" "Das sind ein Hund…." But would a German ask the question that way? I don't think so.)