The chance for getting a trophy is independent from stars for now.

I agree that trophies are too much common, but starred creatures are either uncommon or far more dangerous.

Perhaps a solution would be to have a scalable chance to get a trophy. For instance, 0-deers would have 5% chance, 1-deers would have 20%, and 2-deers would have 50% (vs 50% for all). To be balanced of course (how many trophies to craft a sledge hammer?).