If your dog is about to have puppies, then she's engaged in the propagation of dogs, the creation of new life to further the species.
Propagation has two main uses, both having to do with multiplying something. If it's used in relation to creatures, that means that the creatures are multiplying — having kids. A synonym for this is procreation. You can also use propagation for anything that multiplies and spreads through larger and larger numbers or spaces — from the propagation of weeds in your garden to the propagation of a new idea. In physics, propagation is wave movement.