The Book of Mormon mentions sheep quite a bit. It’s an important symbolic animal. However, there isn’t a ton of evidence of domesticated sheep in the ancient Americas. There’s lots of plausible explanations though, and I’d like to offer just one. I’m not saying it’s the best answer, but it’s one of the answers.
There’s evidence of ancient Mesoamericans lightly domesticating deer. They were considered a sacred animal. And even used for sacrifice.
The Book of Mormon was written for us today, and I can see God allowing the changing of non-important terms or words, unimportant to our salvation, during the translation so that we could better understand the eternal meanings.
Baby deer, fawns, are also just super cute and I can imagine Christ holding one like in this image, treating it symbolically as a representation of us and even as him.
I found this image randomly online. It’s by Shawn Costello and it’s called Jesus with Fawn.