I don't believe so. As I mentioned above, Kipling and King page 350 states that this is the badge "worn in South Africa by the regiment formed in Scotland". The Australians would presumably have worn one of the other two versions and are shown wearing those badges in the illustrations in Southern Cross Scots by John Price. I am puzzled by K and K's referral to the regiment formed in Scotland as the Scottish Horse was first raised in South Africa in December 1900. The Military History of Perthshire records that due to a shortage of recruits in South Africa for the 2nd Scottish Horse in early 1901, permission was gained for recruitment at home and successive drafts totaling 4 officers and 397 men including 309 Scotsmen were sent out to join the 250 Victorians raised in Australia. These presumably are King's regiment formed in Scotland but I have never come across a photo of the badge being worn in South Africa.