gehrke-
I was on the big island in feb and it is a blast. As others have said, get your hunter safety card/letter out of the way and the rest you can take care of when you are there. Read the regs you get from fish and game when you are there and there is plenty of hunting on public land. The regs seem a little confusing at first but a few minutes of study and pondering will get them figgered out. The regs are posted on the web also so you can study ahead of time if you want.
The jungle has lots of pigs around the Hilo side and if you ask land owners will some times let you hunt to rid them of the pests. Never ran into any pit bulls but I am sure it is a possibility. I WOULD be some worried about playing with a big boar the was in a bad mood tho. Sheep and goats are up higher esp in warm wx. More goats on the Kona side. Look around the Pahoa area and an area called the four corners area near Pahoa, lots of hippy types and commune type living, folks that might let you hunt or point you twords somwhere to do so.
Be sure and take a drive up both mountains, the views are SPECTACULAR, and theres huntin up there too. WE saw and got close to sheep on the "power line road" (my buddy didnt see them till too late and spooked them! ;-) ) Lots of bird hunting there too, check the regs.
I brought back some pig and sheep meat from a friend that lives there and - oh my- yummmmmm!
Take good tuff hiking boots for walking in the lava, you'll need them.
Aloha-
Tom