The big thing is to change course.
You (and everyone else with a passive sonar) will know when it gets launched.
A rocket powered
anything is going to generate huge amounts of sound.
Use that to your advantage.

Who ever launches the damned thing will lose your track as soon as the motor lights off.
Don't sweat going to flank speed, remember the other guy can no longer hear you. Likewise, don't sweat the counter measures. You're basically wasting them until things quiet down again.
I'd think a bit about changing course 90-120 degrees
towards the bearing of the "super" weapon. As long as you can offset the bearing to the fish smartly, you may as well pull a banzai move from the old 688i days and close on the launch platform- give
him something to think about once things quiet down.