It is not uncommon for stairs and hallways to be solid surface - i.e. wood or in your case laminate - and bedrooms to be carpeted because people like the cozy feel.

Does laminate work for stairs?

Yes, Laminate will work.

emackey , any reason for laminate over wood flooring?

Not really other than pricing. If I can stain the hard wood stairs to match 1st floor Laminate then, I would probably install wood in the hallway. If not the laminate may be easier to match and use for stairs and hallway.