What should we do if we realise the Queen should have been on the board?
Treat it as covered.

According to these rules:


  96) If the Queen is pocketed by a stroke and is not covered, the Queen shall be taken out for placing. If not noticed by the Umpire or by the opponent, before the next stroke is made, the Queen shall be recorded as properly covered.


In a casual setting, however, I'd take it out and place it before your next turn (so you get the next shot on it).