New Zealand is named after the Dutch province of Zeeland, not the Danish island of Zealand, so I think the answer should be The Netherlands and not Denmark... unless I've misunderstood the quiz!
I acutally did have the Netherlands at first, then did some research and saw the more prominent piece of land with that name was in Denmark. My bad, will be changed.
New Brunswick was actually named after Brunswick-Lüneburg in what is now Germany. albeit by a roundabout way in that George III of England was at the time Prince-elector of Brunswick-Lüneburg