If all you are doing is flying to Brooks to see the bears, you really won't "need" your firearm anyway. All of the private airlines don't allow firearms and its possible that it's against federal law to bring one to Brooks (not sure on that one).
We went about a week ago and it was pretty darn cool. We flew with Beryl Air out of Homer. Call them or anyone who flies out there and ask questions, they're more than helpful.