2-week trip (adventurous early 30s with a 4.5-month-old)

Hi all! We have flights booked early January into Christchurch and out of Auckland. We’re starting to look into accommodations and first want to make sure we’re not trying to do too much. We’re looking at a mix of Airbnbs and hotels, only planning 1 activity each day, and we’ll see from there.

• Christchurch 2 nights (we’d like to do a train day trip to Arthur’s pass, not sure how feasible with an insane)
• Lake Tekapo/Pukaki 2 nights (day in Mount Cook)
• Queenstown 1 night -Te Anau 2 nights (Milford Sound) Travel Queenstown > Auckland
• Taupō 2 nights
• Rotorua 2 nights
• Auckland 2 nights

Thanks in advance!!