Sydney is subjected to Dust Storms from time to time, especially in periods of drought. Most readers would remember the major dust storm of 2009 and also more recently in late 2018. In the Black Summer Fires of 2019-2020, dust was even mixed with bushfire smoke.
On May 22, 1962, north westerly winds blew dust from central Australia into Sydney. While the storm was minor compared to 2009, visibility dropped to less than a mile. I remember in 2009, visibility was down to 100 metres at its worst (akin to fog).
The Daily Telegraph published a full page feature on May 23, 1962 including a large photograph taken from Bent Street, North Sydney showing the city obscured by the dust. The Sydney Harbour Bridge was visible . The distance from the location of the photograph to the Harbour Bridge was about two kilometres suggesting that visibility had dropped to around two kilometres.
The "Darkness at noon" was probably exaggerated.