Although we Vax this was the one we decided not to do. They had the later doses (My nurse confirmed that the birth dose was for that 'period of time' and was not needed for the other doses to be effective.

From the My Vaccination Gov site
The birth dose of hepatitis B vaccine is given to help prevent the spread of hepatitis B virus from an infected mother to her newborn child. This dose is also important to help protect the newborn in the first months of life.

Hepatitis B vaccination is recommended and provided free to children as part of the National Immunisation Program. It is provided as 4 injections: one at birth followed by another 3 doses given at 2, 4 and either 6 or 12 months.
We know I don't have it, our babies are not in care with anyone else, so i dont consider it a major risk in the first months.