How did Katniss show bravery by hunting in the woods?

I suppose being alone in the woods, she did not always hunt with Gale, was dangerous. She could have been hurt by an animal or caught by the party for trespassing.

Even though trespassing in the woods is illegal and poach- ing carries the severest of penalties, more people would risk it if they had weapons. But most are not bold enough to venture out with just a knife. ch 1 pg 6