Can we imagine the cool-headed lawyers of today being impassioned enough to participate in a duel? No, not really, so we must transport ourselves back to the year 1844 ...

note: not THE duel in question, but a depiction of pistol duelling
image source
... the story begins:

full article here
Interestingly, William Brewer had been involved in a previous duel (elsewhere in the country) about four years before this incident; but that time his luck was better and he shot his opponent's wig, without himself being injured in the challenge.
The players in this tragedy:
Hugh Cokeley Ross - originally from Scotland, spent some years in Australia before settling in New Zealand after being caught embezzling funds while working as a Crown solicitor no less. He eventually set up practice, as a lawyer, in Wellington.

image source and full article
William Vitruvius Brewer - along with his brother Charles, were two of the earliest lawyers to set up practice in New Zealand after emigrating from England. Incidentally, their father was a prominent barrister, and their sister Catherine - who also emigrated to New Zealand - was married to a Supreme Court Judge, Henry Samuel Chapman, and who would later take in Brewer's widow Isabella nee Harrison.

image source
Arthur Edward MacDonogh - (various spellings of surname found) was an Irishman who emigrated to New Zealand and became a Police magistrate; and the man at the centre of the dispute around which the challenge was issued. By all accounts, as a policeman, his judgment was sound and sensible.

as signed, from a published newspaper letter
image source
At the Wellington County Court Hugh Ross was defending MacDonogh on a charge of ‘illegally retailing … a certain quantity of spirituous liquors’1 and disputed with William Brewer over whether he had agreed to 'waive a notice' at the trial. A dispute which clearly escalated to the point where a duel was agreed upon, attendee's confirmed, and a place set.
Ross, his 'second' Maj. David Stark Durie, Brewer, and Dr. Dorset (the attending surgeon) were all known to have been on-site for the duel, which took place near Pimble's brickyard - one of the businesses situated along Sydney Street, in the Wellington suburb of Thorndon. (I believe this is the same street as the court building was situated on.)

looking down Sydney St., Thorndon, Wellington (c. 1900)
image source
Apparently, William Brewer discharged his pistol wide of his opponent, so likely never intended to wound or kill him, but was not so lucky in the exchange as he took a bullet to the groin. For a time it seemed he might have been recovering, but gangrene set in and he finally passed away seven days later.
This incident sparked some speculation in the newspaper over the practice of duelling itself, which can be read in full here; while an extract of which reads:

Because duelling was banned by law, no one involved was willing to step forward and tell the whole truth of the matter; so we will never know the full and accurate account of what occurred that day.
Sadly, this wasn't the end of tragedy for the two remaining players. Hugh Ross's daughter Ann Eliza married Arthur McDonogh later that same year, but Arthur had a gambling problem and a long history of stealing funds. One day, eight years after the duel, fearing discovery of his escalating crimes, he took one of the duelling pistols - which Ross had gifted him as a wedding present - and killed himself with it.

Wellington cemetery record
He left behind a shocked friend, and a heartbroken wife and child.
Endnotes
(Incidentally, Catherine Brewer would later have her own tragic story.)
References
Bibliography
https://www.findagrave.com/memorial/186241535/hugh_cokeley-ross
http://mp.natlib.govt.nz/detail/?id=4285&l=en
https://www.nzgeo.com/stories/duel-at-20-paces/
https://nzhistory.govt.nz/pistols-at-dawn-deadly-duel-in-wellington
https://paperspast.natlib.govt.nz/newspapers/NZGWS18440306.2.5
https://paperspast.natlib.govt.nz/newspapers/NZGWS18440309.2.5.1
https://paperspast.natlib.govt.nz/newspapers/NZGWS18440309.2.5.1?query=duel
https://paperspast.natlib.govt.nz/newspapers/NZCPNA18421007.2.7?query=hugh%20ross
https://paperspast.natlib.govt.nz/newspapers/NZCPNA18430421.2.7?query=macdonogh
https://paperspast.natlib.govt.nz/newspapers/NZCPNA18430721.2.13?query=macdonogh
https://paperspast.natlib.govt.nz/newspapers/NZGWS18410731.2.6?query=brewer
https://teara.govt.nz/en/1966/duels
https://teara.govt.nz/en/biographies/1m34/mcdonogh-arthur-edward
https://wellington.govt.nz/services/community-and-culture/cemeteries/cemeteries-search