We want to hire a camper van at the end of September . Picking it up in Christchurch but dropping it off in Queenstown . Can anyone suggest which companies may allow this ?

You need to work backwards since Queenstown has fewer campervan companies. Search "campervan Queenstown". Find which companies are there. Those that are there are highly likely to have a depot in Christchurch. Most any company that has a depot at both ends will allow the one-way hire.

It will need to be one of the big ones. Start with Maui. If they dont, they might point you to someone that does.