Are you sure its Australian? It's not a unit/sub unit I have heard of before.
Maybe USA? The Americans also had a 1st Division in France during WW1.
Edit: Though I did just read this on wiki.
"The 13th Light Horse Regiment and one squadron of the 4th Light Horse Regiment served on the Western Front, first as divisional cavalry squadrons for the 2nd, 4th and 5th Divisions, and then as the I ANZAC Corps Mounted Regiment. A squadron of the 4th provided the divisional cavalry squadron for the 1st Division and one of the 14th Light Horse Regiment for the 3rd Division. In combination with New Zealand mounted troops, the squadron of the 4th became part of the II ANZAC Corps Mounted Regiment. After the Australian Corps was formed in November 1917, the I Anzac Corps Mounted Regiment became known as the 13th Light Horse Regiment again."
From the AWM:
https://www.awm.gov.au/collection/U51038
So possibly a squadron of the 4th Light Horse Regiment?
Mick