welcome to FT!
I have flown THAI and Singapore, and both are good in biz.
Noting the youngster, the fewer the stops the better in my own experience and long layovers can be a hassle.
I'd be tempted for the TG flight as once you make it to AKL, it is just the one 12 hrs journey! THAI are excellent with kids.
Pricing can be very variable, and depends a lot on when you are flying.
Also consider if flying CHC-SYD-BKK on NZ/TG is worthwhile. The A346 from SYD to BKK is nice.
Although I haven't flown, I hear that the PE on QF is better than on BA. Be careful as some flights sold with QF flight numbers are actually BA aircraft and vv.
Cheers, TK