Can an all nighter for just one night be unhealthy?

No, not at your age, But you may be quite tired the next day. Best wishes.
Sort of. Anything in moderation may be tolerable. Disrupting sleep and altering natural day/night sleep/wake cycles has harmful effects - but the consequence of doing this for just one night would be so small as to be undetectable. Unless you get into a car accident when you fall asleep driving after being up all night.