According to ESPN, Charlie Batch has the highest single game QBR rating of all time -- a perfect 100.  That was in September-

12/17, 186 yards, 10.9 AVG, 3 TD, 2 INT

Since then ESPN changed that rating (I assume because of embarrassment since anyone who knows anything can tell you that's not a spectacular game, certainly not the best ever.)

The reason the QBR rating is not immediately available during and after the game like passer rating is because analysts go through the film and make determinations on who is at fault for missed passes etc.  Something they could not know without knowing the play.  

QBR is an opinion, not a statistic.