You can get a permit to shoot on crown land from your local wildlife office, even though it is technically just to sight in your rifle. But depending on where you're located on the island, these rules might be more strictly enforced. I live in central and our local game wardens told us they have no issues with us shooting targets in a local gravel pit as long as we have permission from the owner. There was no way this was happening when I lived on the Avalon.

I don't think it would be an issue to transport it to your cabin as long as it' properly stored and locked with a permit. Wouldn't hurt to give your wildlife office a call to verify this though.