He was employed by Sir Thomas Brisbane to work as astronomer's assistant at his private observatory, once located at Paramatta (now named Parramatta), New South Wales, about 23 kilometres (14 mi) west of Sydney during the 1820s and 1830s.

Dunlop was mostly a visual observer, doing stellar astrometry work for Brisbane, and after its completion, then independently discovered and catalogued many new telescopic southern double stars and deep-sky objects.

Soon after arriving, Brisbane almost immediately started building his observatory at Paramatta (original spelling), now named Parramatta, and it was Dunlop who was employed to do the astrometric observations for a new accurate southern star catalogue.

For there he began organising his own observations of double stars and deep-sky objects for the next 18 months, in which he constructed telescopes and other equipment for his dedicated southern sky survey.

Sir Thomas Brisbane, before finally departing Sydney for the last time in December 1825, arranged to sell all of his instruments to the Government so the observatory could continue to function.

Sir John Herschel, when making the presentation, spoke in the highest terms of the value of the work done by Dunlop in New South Wales.

These two detailed astronomical papers were received with many accolades from his peers, which lasted until about 1834, when his observations were able to be scrutinised by John Herschel and Thomas Maclear in South Africa.

Only then were the various flaws of his observations revealed, and the time spent in the zenith of popularly, then dwindled to fierce criticism and personal rejection especially from the British astronomical community.

He arrived at Sydney on 6 November 1831 and found the observatory in a deplorable condition; rain had entered the building, roofing plaster had fallen down, and many important records were destroyed.

He first began with Alpha Crucis / Acrux, the brightest star in the constellation of Crux, also commonly known as the Southern Cross, then systematically searched for all the others.

Herschel also was first to designate all the Dunlop double stars to begin with the Greek letter "Δ", which persists in many amateur observational references.