Sydney Gazette, 11 August 1825
Not an occupation I can find out much about. Feather curlers were used by milliners to produce suitable feathers for their hats. However, if you read down through these advertisements you’ll see they’re offering a different, if related, service. Bearing in mind here, hats were necessary fashion accessory, and if yours was looking a bit run down, you could get it cleaned and the feathers refreshed or, presumably, replaced, without the expense of buying a new hat. You could even get feathers dyed and new trim added to help a favourite hat become fashionable again.
As above, the service was often provided as part of a dressmaking or millinery business, but at other times, particularly later in the century (see the bottom ads), feather cleaning, curling and dying is the whole business. I guess it was a good occupation for a woman wanting to support herself in a smaller city.