There's always young passengers aboard NCL ships. I would venture to state there's passengers aboard all NCL ships ranging from ages less than one to over 80 years in age.
The percentages of those vary at different times of the year. During school holidays, there will be more families with kids aboard, less during school year. But you'll find school age kids with families aboard ships year round.
To add, the longer the cruise, the higher percentage of retired passengers you'll see. Passengers still working to earn a living don't wish to use all their vacation days on one cruise. So they tend to book shorter cruises around a week in length or shorter. But you'll will run into passengers still in the work force who prefer and book longer cruises.
So go ahead and book the cruise you wish to take, there will be some younger passengers aboard in late January, but not as many as you'll find in June, July, or August.