It shouldn't be too hard to implement this either in your theme or as a layer plugin. Run a database query that returns the number of questions posted on the current day (or within the last 24 hours, whichever you prefer), and display that number wherever you like.
The query would look somewhat like this for the number of questions today:
WHERE type = 'Q' AND date(created) = curdate();
or like this for the number of questions in the past 24 hours:
WHERE type = 'Q' AND timestampdiff(hour, created, curdate()) <= 24;