With the exception of Quartermaster Laycock, seen in the left foreground of the painting below, any images of the New South Wales Corps I've seen show the men wearing stovepipe shakoes as in HaT's or Emhars peninsular War British infantry rather than the brimmed round hat.
This painting also shows them wearing breeches and gaiters, don't now where you'd find figures like that unless you body swapped them onto French legs, but other images from the slightly later Rum Rebellion show them in trousers without gaiters.
With the NSW Corps leaving for Parramatta to deal with the rebellion Sydney was garrisoned by sailors and marines from HMS Calcutta and local militia. HaT's British sailors and Marines would help if you wanted these.
In the attack on the rebels the Rum Corps were also joined by civilian militia. Perhaps some figures from HaT's Spanish Guerillas that don't look too Spanish would work.
I don't know of any Cavalry from this period.
Images from the Rum Rebellion:
The officer in that last pic is the same Captain Johnstone who led the attack on the rebels at castle hill.