The expressions “this here” and “that there” immediately before a noun are nonstandard. In standard English it’s not “this here dog” or “that there cat,” but “this dog” and “that cat.” Less casual is “this dog here” when you are emphasizing the exact item you are indicating as contrasted with others.

Of course “this here” and “that there” have standard uses when they are not followed by a noun: “put that there,” “I left this here on purpose,” “I’ll say this here and now,” “there’s a space for this here.”