If these were Central Asian nomads and they were tossing around a dead sheep / goat carcass on horseback (as they like to do), nobody would complain. Unless (I suppose) they were doing it in NZ, or the goat was a NZ citizen (as I understand it, there is a good deal of fondness for sheep there <wink>).
Desecration has different meanings for different people, some would think organ donorship is terrible too. And others would condemn burning a body (or for that matter feeding it to worms). Myself, I am for recycling it (feed the vultures at the zoo).
Tossing a dead rabbit is not worse than shooting a live rabbit, from the rabbit's point of view. What happens to it after death is immaterial, if the kids enjoy the contest and there are no health concerns, let them have their fun.
A dead body is just that, a piece of meat, unless you knew it personally (a pet) or were related to it (a human). It is somewhat disrespectful to toss a dead animal, but I can see the benefits too (the kids will be more inclined to think of rabbits as vermin).