There is no 9–6 overlap. Stretching to 07:00–21:00 on both sides gives you 07:00–12:00 Doha time:
07:00 you → 16:00 Wellington
08:00 you → 17:00 Wellington
09:00 you → 18:00 Wellington
09:00→18:00outside Wellington working hours
10:00→19:00outside Wellington working hours
11:00→20:00outside Wellington working hours
12:00→21:00outside Wellington working hours
13:00→22:00outside Wellington working hours
14:00→23:00outside Wellington working hours
15:00→00:00next day · outside Wellington working hours
16:00→01:00next day · outside Wellington working hours
17:00→02:00next day · outside Wellington working hours
Working hours assumed 09:00–18:00 local. Offsets include daylight saving where it applies, so this shifts through the year.