Here's the website of the National Library of Australia And a photo of it:
Someone in Canberra needs to check it out. Here's a Map
The "Kenya Dominion Record" might be a newspaper.
But I don't trust drive by posters, and JimColt still hasn't posted anything else after signing up on the 5th. Plus no one, including me, seems to be able to find any "Kenya Dominion Record". If it was a newspaper, surely there would be some reference to it somewhere. WAIT ONE I found a reference to the Kenya Record, which is called a "Journal/Newspaper", but only published from 1978.
Here's another possible source for the same information.
Annual report of the Registrar-General
But in either case, you'd have to be in Canberra to go look at them. Best call ahead as they say all the pre 1990 stuff is "off site", so you might to either go "off site", or they might go get it for you, which would take time.