"Nông trại động vật"
Same in English. We don't say "animal farm" to distinguish from a farm that just grows crops. Or at least not generally. Maybe farmers have their own more specific terminology most of us don't use.
Update: The farms I'm used to typically specialize in one kind of animal and in that case we do indeed have cattle farms, dairy farms, sheep farms, and pig farms. Farms that have more than one type of animals tend to be small farms that also have some crops and I'm not sure what we'd normally call those if we had to qualify them.
In Vietnamese, attributive modifiers always follow the main noun. This means that in this sentence, "nông trại" is the main noun and "động vật" qualifies it.
In English it's the other way around: attributes precede the main noun. So, since "farm" must be the main noun and "animal" its attribute, "animal farm" is the correct order.
Also please note that, while English doesn't allow nouns to be attributes (in fact "animal" in this case is an adjective), in Vietnamese this is quite normal and "động vật" is indeed a noun, even when used as a modifier.