Blue books were used to send data back to the Colonial Office in London about how the Colony was doing. Every Colony had to send one every year, including Fiji. From what I can find out they started in 1876 and finished in 1940. The task usually fell to the office of the Colonial Secretary.
Blue Books give a snapshot of the country in time, and since the snapshots are taken every year you can get an idea of how the country is developing over time. Revenue and expenditure, population, education, imports and and exports, agriculture, total grants of land, gaols and prisoners, criminals, lunatic asylums, hospitals, charitable institutions, banks, railways and roads; nothing was overlooked. The British Government was paying for this colony and it wanted to know what it was getting for its money.
Blue Books also list government employees. All of them. So if your person of interest was working in the government or holder of a recognised native office you can follow him or her over time to see what position was held.
The headings listed in the Contents page for 1890 were:
Here is a piece of a random page from the List of Officers on page 77 of the 1890 edition:
You can see everyone here from the Chief of Rotuma and the Buli Bua down to a clerk in Suva Hospital and another in Levuka Post Office. The numbers in the right column refer to the page in the report where the job is described. I’m sorry I didn’t check the page where the Chief’s jobs are described!
Another interesting section is the answers to set questions about prisons:
As onerous a task as it must have been for the Colonial Secretary and his Office to compile these reports every year, we historians must be grateful that they did so.
The Mitchell Library in Sydney has a collection from 1890 to 1940.
The National Library of Australia has them on microfilm from 1876 to 1940 with some gaps.
The University of Queensland has a run from 1889 to 1940.
Other Australian libraries have shorter runs. Check Trove for details.