Is it a reasonable trip to start from Christchurch, head up Kaikoura coast to Abel Tasman, come down all the way along the west coast , then end the trip in Queenstown ?

I have seven days on the south island. Is it a reasonable trip to start from Christchurch, head up Kaikoura coast to Abel Tasman, come down all the way along the west coast to Milford Sound, then end the trip in Queenstown (where we will fly out)? I've tried to measure travel time etc., but I've never driven in NZ, so it's hard to say. Also, we are renting a campervan so it is much more compact, which means faster travel? They often have a portable toilet so we can camp whenever. Is that just too much driving? Our plan is to do something each day, such as: Drive to Fox Glacier for the evening, hang out/have dinner. Then the next morning, skydive then drive to the next place, etc.