Are you taking your own car accross on he ferry from Welington, or fly and hire car/campervan?
We did a 7 day tour last year, from christchurch south, each night at a different place and still did not get as far south as Invercargil, a lot of driving but plenty beautiful scenery/places to stop and look at as you travel.
Prior to going we got some some maps and mileage/time charts from the library and planned a route which we thought was not too ambitious but covered a lot of what we wanted to see, in the end we were happy with our plan but it did highlight to us that we need to allow more time on future trips so we can relax and enjoy the beautiful south island.
So in your situation my advise would be to look at exploring a smaller area for this trip, and I suppose the actual area would be determined from your start point and mode of transport, from that you will plan, I am sure, further trips for the rest of the island (sorry I cannot advise on the young one, well not these days anyhow)
Enjoy your trip.