Yes, I would pot it up quickly in a tiny seedling tube. Keep it lightly moist but not soaked.
The tiny ones on the mother plant I would remove them with a chunk of cane each. Do the same with these as you did with the other keiki. I have managed to grow plants on like this.
I would unpot the mother plant and try to save the new shoot, if you leave it with the dying plant it could well die too.