9-Day Itinerary - Queenstown to Christchurch

Hello all,

My partner and I will be heading to New Zealand in the middle of September.

We fly into Queenstown and spend 9 days on the South Island, leaving from Christchurch. We've done the research and want to finalise our itinerary, and would love a third-person's perspective on it.

Here's the plan so far:

Day 1: Arrive in Queenstown (Sleep at Queenstown)
Day 2: Queenstown (Sleep at Queenstown)
Day 3: Take bus to Te Anau (Sleep at Te Anau)
Day 4: Take day tour to Milford Sound (Sleep at Te Anau)
Day 5: Bus to Queenstown, rent a car, drive to Glenorchy, then drive to Wanaka (Sleep at Wanaka)
Day 6: Hang out in Wanaka, drive Lake Pukaki + Mt Cook (Sleep at Mt Cook)
Day 7: Mt Cook (Sleep at Mt Cook)
Day 8: Mt Cook (Sleep at Mt Cook)
Day 9: Drive Lake Tekapo + Christchurch (Sleep at CHC)
Day 10: Fly-out from Christchurch to Auckland

Questions are:

1. Is this a good itinerary, or do you have any suggestions?

2. Bus & Car Rental. We plan for Day 1 - Day 4 to only take buses, since we heard that it's unwise driving to Milford Sound because of the avalanches/ice. We then start renting a car on Day 5 from Queenstown and drop it off in Christchurch at the end. Is this a good plan?

3. Day 5 & Day 6, is this ok or too tight? I don't imagine we'll see any of Wanaka on Day 5, but we're hoping half of Day 6 is enough before the drive towards Lake Pukaki/Mt Cook. The alternative is to not see Pukaki on the way to Mt Cook but afterwards when we leave it to go to Christchurch on Day 9.

Thanks in advance!