Translation:The elephant's child is not small.
Is το μοσχάρι του ελέφαντα OK? I found it in Mandeson's dictionary. Words such as μόσχος (masc or fem.) and μοσχάριον (neut.) were common in ancient Gk (preindustrial) agricultural world. I'm not aware of παιδίον or παῖς ever being used for anything other than a human child or slave in ancient Gk. I'm guessing that DL includes it here in this way as vocabulary building a little bit at a time in an effort not to inundate people with agricultural terms.
No, "μοσχάρι" is a cow's calf. It's true that, when referring to animals, it's better to refer to their babies as "μικρό" instead of "παιδί".
Το μικρό του ελέφαντα"=Ελεφαντάκι
"Το μικρό της αγελάδας"=Μοσχάρι
"Μοσχάρι" is a pejorative term when referring to people.
It doesn' t say "the baby elephant," it says "the elephant's child" /"the child of the elephant". We need to translate not interpret.
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In case you mean "child" is too generic a word and sounds like someone's referring to a human, then yes, it does sound a bit weird. On the other hand, there's no specific word for that, so what you'd probably get to hear would be "το μικρό του ελέφαντα", literally meaning "the elephant's little".