"Julia is not a cow, Peter."
Translation:पीटर, जूलिया एक गाय नहीं है।
I think you are mistaken. I am a native Hindi speaker and I cannot instantly think of quite what rule you might be referring to. In this sentence, in any case, the है is definitely required. (To be exact, I can think of instances where you might do without the है in this or a closely-related sentence, such as someone protesting, "जूलिया कोई गाय नहीं, पीटर!", in the middle of a conversation. But as a standalone sentence, this definitely needs a है at the end.)
If you could state the rule you are thinking of more precisely, perhaps I or someone else here could let you know if it's a correct one or not.