He conducted a number of exploring expeditions; was responsible for one of the earliest published records of the language of the Aboriginal Australians of the Perth area; and was the author of Diary of Ten Years Eventful Life of an Early Settler in Western Australia.
He graduated in law in 1820, and spent the next six years at the Irish Bar, but seeing little prospect of advancement he decided to pursue a judicial career in the colonies.
Moore sailed from Dublin bound for Western Australia on board Cleopatra, arriving at the Swan River Colony on 30 October 1830.
Moore also obtained half of William Lamb's grant in Upper Swan by agreeing to undertake the improvements necessary to secure the entire title.
The information Moore gathered on this expedition guided him in relocating his inland grant to an area with vastly better pasture land.
In particular, from March 1835 he continually opposed Stirling's proposal to raise a troops of mounted police to protect against attack by natives.
In 1842, Moore's dictionary was published under the title A Descriptive Vocabulary of the Language in Common Use Amongst the Aborigines of Western Australia.
Over the next few years, he vigorously opposed a number of proposed measures intended to soften the effects of the recession on leading land holders.
His views began to attract ridicule both in the Legislative Council and in the press, but he remained influential as he had the confidence of successive governors John Hutt and Andrew Clarke.
The government of Irwin and Moore was extremely unpopular; Battye (1924) writes "every administrative act was viewed with suspicion. ...
Long years of depression and struggle had made the colonists pessimistic, and ... they threw the blame on the Government of the day."
In about 1878, the editor of The West Australian, Sir Thomas Cockburn Campbell, sought and was granted permission to serialise Moore's letters.
Stannage (1978) writes that he died "apparently friendless", and Cameron (2000) adds "it was a sad end to a worthwhile colonial career."