just a thought on how you might bump up the 'thousand or more'.

NK was a very traditional society - an aristocracy, birth marriages, hereditary rulers, etc.

In many traditional earth cultures (e.g. England) it was customary to refer to population in terms of the number of "households" rather than the number of individuals. "Household" meant 'extended family plus servants living within the household. So if Zara was using the term that way you could turn that 1000 into 10, 000 or so,

Another possibility - in traditional, hierarchical social systems, many individuals who we would count "in" weren't counted in because they weren't considered to be fully "human". e.g. peasants in medieval Europe, slaves in the original American Constitution, women in practically every Earth culture until the 20th century. So you could assume that Zara, an aristocrat, could mean '1000 or more *'aristocratic* families, reflecting her social bias.
(OT - trying to recall how many were part of the "Social Register" in 19th century New York , or was it Boston?)

All these 'creative' accounting suggestions still end up with a small population though. Nevertheless, given a harsh environment it would be enough to ensure survival unless they were attacked by a superior military force.

Also, given NK's superior technology - think of the cloning possibilities laugh (Replicants!)

c.