Because of the offsetting policy reactions, the real federal funds rate would be likely to remain approximately constant during this chain of events. If it did, the nominal funds rate would first rise and then fall with the inflation rate itself. While not a perfect outcome, this targeted intermediate approach is probably about the best that can be done.
Were policy to try to avoid any rise in unemployment, the initial oil price shock might get passed through to continuing inflation. Were policy to try to avoid any rise in inflation, the movement in unemployment would be substantial. The best approach is likely to be to accept some temporary rise in both inflation and unemployment, with the increases being based on underlying objectives.