I've been looking for something for her to call him - I searched on google for russian diminutives, and then I thought of buck = deer, so I did some searching for making diminutive nouns, and through that I believe that olenik may be the proper diminutive, but I know that's also a surname so I'm not certain if it's exactly accurate.
Basically, I'm just wanting to know what the proper diminutive is for "deer". But I'm also open to any other suggestions for what Nat might call him???