I'm betting that there is a St James Church in just about every parish in Oz. There is one in Morpeth, which is 20 miles north of Newcastle, New South Wales, where I live. If you looked in the white pages or yellow pages you could search each listed area and it might take a couple of hours or more, but you should find all of them if you are thorough.

Do you have any more info on the area or even state that the church was in?   
Could you contact the organisation which arranged the child sponsorhip programme?

I just put the search terms "orphanage" & "Taegu" in Google and got a few sites. This is the first one I looked at.

Humanitarian efforts during the Korean War

Helen