I think the National Cabinet has decided that the distribution will first go to healthcare professionals, followed by aged persons and people working in critical sectors.
I would say if Pfizer can provide 10 million doses from March, and millions from AstraZenaca possibly from January, we could see 30 - 40% of the population vaccinated by Easter, depending on the process of delivery from the Pfizer vaccine. If that's the case, I don't see why travel will still be banned from 17 March.
Yes I would agree that we need the vaccine to first roll out in order for borders to reopen, yet I would say we could be able to safely open the border to selected countries once we have the most vulnerable vaccinated, because we can ensure by then the probability from dying will be a lot of lower across the population.
I would propose once vaccines are available and approved, I predict this is the sequence in which the borders will reopen:
January/February - NZ and potentially Pacific Island countries
March/April - SE Asia, Hong Kong and Taiwan etc.
May/June - North Asia
Europe and US may need a higher rate of vaccination across the population to bring the virus under control, in this case, we might need to wait until later in 2021, yet I think Christmas in Europe/US in 2021 may be possible, depending on the speed of delivery of vaccines.