Assuming the train travels about as fast as modern trains, and assuming that it took a fairly direct path, three days of travel is roughly the time it took me to take a train from Chicago to California.  This is ~ 2000 to 2500 miles -- and that's after leaving the city itself, which I suspect is massive, given that the city seems to include most of the populated area of Varya, more like a city-state than merely a simple city.

Assuming a generous 15 miles a day for the children -- who not only have shorter legs than the adult hikers I'm using for reference but were unused to hard labor, and who likely didn't have enough supplies at the start for the entire trip, and so on -- the trip would take ~ 133-167 days, between a third and a half of a year.  Given these conditions, I expect the trip took half a year or more, perhaps even a full year.  That is one AMAZING child, to have planned it and gotten the two through it.  And kept them all from freezing in the process.

Wow.