There is already a word that can be used for "owl."  

It's {lIr}, which is some sort of Klingon nocturnal bird.  

So an own on Earth would be a {tera' lIr}... or just {lIr}.

For "bunny"...  There's a Klingon animal that's sort of like a rabbit called a {cheS}.  

So a rabbit on Earth would be, I guess, a {tera' cheS}, though, in context, {cheS} is good enough.  

And a "bunny," I supposed is a {cheSHom} or maybe {cheSoy}.

{cheS} is a word no one besides you and me and Maltz knows about...yet.  

I'll inform everyone else at the qep'a' later this month.