Hi carloslen,
I should explain that 'Length of Residence' in ITM notices only meant how long the applicant had been in the district where the notice was registered, not their length of time in the country. I've noticed that many applicants seemed to have "3 days" as their length of residence, meening that they presumably travelled to the area for the marriage.
In the case of Frances Brown, you might assume she had arrived in Dunedin as an immigrant a year earlier, but even that could be incorrect (her family might have simply moved to Dunedin from elsewhere).
Niels' arrived in NZ in 1863 on the vessel Lawrence Brown: Niel OLSEN aged 28, single, occupation miner. From Hobson's Bay VIC AUS on 23 Oct 1863 to Port Chalmers Otago. I presume it would have arrived in Otago within couple of weeks.
I think you should contact Dunedin's Early Settlers Museum for any record of the arrival of Frances' father, Thomas Francis BROWN.
Regards, riley