With just 8 days I would go to the South Island and skip the North Island, unless you want to go to a specific destination. Having a campervan allows flexibility, even if you stay in DOC, council, or holiday park campgrounds.

Rankers.co.nz lists most of the companies available and there are a wide range of vehicles. I would rent one from Christchurch to Christchurch/Queenstown, many companies are only in Auckland and Christchurch. Now is a good time to book for December, prices probably won’t get cheaper and many places give an early bird discount. Some smaller places have a 10 day minimum as a heads up.