Mumma B - Vit K is given at birth as a child is born with very little or no VitK. Vit K is responsible for blood clotting primarily. The injection is given to cover the risk of the infant suffering a haemeroging (sp?) disorder that can occur in the first month after birth. It is a very serious occurance, however it is also quite rare. (The stats are available if you look for them)
Vit K is fat soluble, meaning it can be transmitted through breast milk. So it can be passed in some quantity to the child immediately after birth.