What is the use of this object in the cockpit of a Bombardier Dash 8 Q400?
It is a mechanical checklist where each item on the list can be flipped to indicate that is has been checked. You can see it in operation in this YouTube video (which I believe is where you got the image from). Each of the 6 stacks can be extended to check the items and then collapsed again in order to not obstruct the pilot's view.

It is not a default part of the Dash-8 Q400. As far as I know, Qantas is the only airline using it.