playBunny: I can't imagine it's impossible actually. All it would take is a quick check at the end of the turn, if the next player can't move then roll the dice and move for that player (using the current code but calling it now instead of waiting for a player action).
I don't think it breaks the design so much so as to make it so very difficult to code. On the other hand I won't know for sure unless I see the code.