The Tilmouths are a v/very large family group in Alice Springs and surrounding area.
I suggest contacting the Alice Springs Public Library mailto:library@astc.nt.gov.au and the Alice Springs office of the NT Archives mailto:nt.archives@nt.gov.au as both of these have extensive information on people in Alice Springs. Alice Springs wasn't that large in the late 1940s and early 1950s (following WWII - when it had a large military population).
Stuart