I wasn't aware of that dagger before, I am at first floor now.
Am I able to get the dagger? or It is necessary to restart a new game?

You have to restart a new game to get it.

I would recommend trying the game without it though... while it's not the best weapon in the game, it's close, and having it at the beginning can make the game pretty boring. The first few levels are tough but if you can get through them it gets a little easier.

thank you