Frank Armstrong served in two units during the Boer War :

 Prince of Wales Light Horse

3rd New South Wales Imperial Bushmen

The uniform pictured is that of the New South Wales Imperial Bushmen as it uses black cock plumes on the slouch hat.  These black feathers were used by New South Wales mounted units prior to the First World War.  Queensland mounted units wore the distinctive emu plumes during the Boer War which were later adopted by all Light Horse Units in 1915.

Information from ISS Information, Australian War Memorial