If any of the children were born in Scotland in 1855, it’s worth viewing the birth certificate on Scotlandspeople. 1855 was the first year of civil registration in Scotland and in that year only, the certificates contained a lot of extra information which was dropped subsequently due to it being too much work. 1855 birth certificates give the ages of both parents, their places of birth and the number of children born to them, alive and dead.
The famine may have been a factor in your family’s decision to move to Scotland, especially if they were labourers, but I suspect they left for the same reasons that 2 million others did. To find work. Ireland has very few natural resources (no oil, coal, iron ore etc) and so did not benefit from the industrial revolution in the 1800s, the way Scotland, England, the US, Canada New & Australia did, which created hundreds of thousands of comparatively well-paid new jobs in new industries (coal mining, steel making, railways, ship building etc). So that was a big pull factor. There had also been a huge population explosion in Ireland going up from about 3 million people in 1750 to 8 million in 1830. There simply weren’t jobs for all those people. In much of Ireland the only employment was subsistence farming topped up in Ulster and one or two other areas with a bit of linen weaving. And then the straw that broke the camel’s back, along came the famine, numerous times throughout the 1800s. The worst period was when the potato crop failed almost completely 3 years in a row in the late 1840s, and then partially several more years after that.
Other factors led to the continued emigration too, eg early mechanisation on farms. With new machines to turn the soil and plant seed, farmers no longer needed an army of agricultural labourers to help on the farm. So those jobs were rapidly disappearing. Likewise mechanisation had led to linen factories being set up in places like Belfast. These made home weaving uneconomic and so also upset the labourer’s family economy. Agriculture was the biggest single employer in Ireland, but it was mostly a barter economy. Few people had any ready cash save what they could make from weaving or any government sponsored work such as building new roads. So when the opportunity arose to get jobs with a regular wage packet, as opposed to a few pence from your father each week, the decision to migrate wasn’t really all that hard to make. So it was as much about economic betterment as anything. The famine wreaked havoc in most of Ireland but in Co Down, a comparatively wealthy county, it wasn’t too severe so I would say it was less of a reason for your particular ancestors leaving than it was for others elsewhere in Ireland.
There was a massive tide of emigration from Ireland all through that century, including long before the famine. All the famine did was speed it up. (After Scotland and England, the USA was the most popular destination for emigrants with about 40 to 50% choosing it. Only about 5% of Irish emigrants chose Australia and New Zealand, possibly due to the costs and length of the voyage).
Ending up in New Zealand via Scotland is called stepped migration. It was very common. The move to Scotland probably enabled them to earn the fares to New Zealand.
Co Down was heavily settled by Scots. One way of analyzing it is to look at the 1901 Irish census. There were 290,000 people in the county. 76,000 were RC (so mostly native Irish), around 126,000 Presbyterians and related denominations, and the rest were Church of Ireland and other denominations. So even 400 years after the first Scots arrived Presbyterians remained the majority denomination. (And many of the Church of Ireland people were of Scots origins too, notably those from the Scottish Borders. Border Reivers, as they are known). So Presbyterianism was (and still is) the main denomination in Down. Probably over half the population there today are of Scots origins.