“It is understood that the Minister's action [banning aerial photography of defence installations] followed certain confidential reports relating to the mysterious aeroplanes reported over Darwin in the early dawn and at night recently, it is now known that they belonged to another Power, and it is thought that aerial photographs of coastlines and certain parts of the Northern Territory might have been their mission” #UFOBotNews

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This historical Australian newspaper article contains the keyword "mystery aeroplane": 25 Feb 1938, 'Our Sydney Letter NOT SO CONFIDENT': http://nla.gov.au/nla.news-article100799625

botsin.space
This is a sequel to the sighting of a mystery aeroplane seen and heard over Darwin in early Feb 1938, which was variously theorised (and mostly ruled out) as being RAF, RAAF, US Navy, opium smugglers and - of course - Japanese: https://airminded.org/2012/01/04/anxious-nation-ii/ But the OP is the only link I can find with the photography ban, though the timing (about a week after the Darwin aeroplane was reported in the press) is certainly suggestive: https://trove.nla.gov.au/newspaper/article/264901751
Anxious nation? — II – Airminded