I however do not recommend that you get a camper. If you do not have the confidence in driving a large vehicle, then don't push yourself. NZ roads can be hard and very winding for inexperienced drivers. If you plan on the Milford Road, there's a section of the journey that is quite winding.
Your drive from Queenstown to the beginning of Milford road will be around 3 hours. And from there to the sound - a further 2-3 hours depending on how frequently and how long you stop to check the attractions. The cruise is another 2 hours or so. So a trip to Milford from Queenstown usually start off early and ends in the evening.
The largest camper is a 6-berth (i.e 6 adults) so it is in no way capable of fitting your group together. You will need to get 2 campers, something I think a lot of people advising you have overlooked.
Btw, such a camper is quite big and you do not just have the issue of driving, you also have the issue of parking. There are limited parking lots available for motorhome vehicles of such size in Auckland and bigger cities. It is not a problem in South Island towns but in Queenstown you won't be able to park in a convenient location within the centre. Or you can leave the vehicle at the holiday park.
This is......if camping (in a vehicle) is your idea of a holiday. Although I enjoy the concept of camper holidays myself (I've done it twice) I realize it is not for everyone.
If you find the cost of renting a passenger van too much (have you checked other websites?), then I would suggest getting 2 cars for renting. An older car with some mileage on it would generally be from 35 per day with standard insurance.