Is your reply in reference to Finnish or English? As a native English speaker I would say bunny doesn't mean a young rabbit in the way that kitten means a young cat and puppy means a young dog. It is more like an informal and slightly cutesy term for a rabbit.
The question is whether this is the case in Finnish. Is there a word in common use for rabbit other than pupu, and if so how do we know when to use it instead? Is there a reason this course is translating pupu as bunny and not rabbit?
Yes, I agree. A bunny is a rabbit, regardless of age, but it's just a cutesy term. Which is why one doesn't eat bunny stew...
In Finnish, bunny = pupu (whether Easter or real), whereas rabbit = kani or kaniini. The friend of Nalle Puh (Winnie-the-Pooh) is called Kani.
Note that rabbits aren't an indigenous species in Finland (except maybe on the Åland islands?). The couple of different species of "rabbit-like" animals in the forests in Finland are hares. But in the last decades, escaped or freed pet rabbits have built up (sometimes quite large) colonies in some Finnish cities. These are usually called "citykani". They destroy parks and have even been known to spread diseases, and have thus become a great example to use when explaining the concept of invasive alien species.