Hi Jan,
    with reference to your question about how a painting from the Caribbean might have ended up in Australia, this extract from Wikipedia's entry on St Lucia, a suburb of Brisbane, might be of interest.  I believe that a number of sugar planters moved to Queensland.
Jon

'Sugar plantations were established in the area in the 1860s. The suburb derives its name from William Alexander Wilson, who purchased and subdivided one of the plantations for housing in the 1880s. Wilson, born in St Lucia in the West Indies, named the housing estate St Lucia because the cane plantations in the area reminded him of those in his country of birth.'

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From: The Black and Asian Studies Association [[log in to unmask]] on behalf of Jan Marsh [[log in to unmask]]
Sent: Wednesday, 19 June 2013 6:09 PM
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Subject: Any Ideas?

it looks to me more a portrait of the parrot than the lad -  that is, it's not firstly a portrait of him, although the artist will have painted from a model who had been 'cast' in this role and dressed appropriately.   however, the model probably didn't pose with the bird, as it is not really perching on his hand, and the parrot could well have been painted from a  stuffed specimen or an ornithological illustration.
 Pictures of attractive young attendants exotically costumed are quite common  and the genre persisted well into 20th century.
if the  parrot species can be identified, this would help in guessing where the painting was produced.   Another clue is possibly in the provenance not from Francis Peek but Lady Peek [his wife?] and more specifically her father Robert Kirkwood who was  Jamaican-born chair of Jamaica Sugar Manufacturers and significant figure there .  if the parrot is Caribbean and the landscape background also, then the picture could have been done in / or for Jamaican market.  how did it fetch up in Australia?