There's no reason to bring your firearm with you to get it registered because you don't actually have to present it to them until you go hunting. With that said, if you intend to hunt the same day you register your weapon, i believe you can bring it on the installation the same day you register it. Things change of course, and its best to call ahead, but that was the status as of last year.
Questions about hunting out there, just call the local Bio in Region 3 and he'll either give you info or put you in contact with the biologists on the installation.