The National Archives of Fiji is working on a searchable list of Girmitya. All the names, from all the immigration passes and other records are being transcribed and posted online. These lists can also be downloaded as PDFs for you to look through offline later.
The online list consists of persons name, father's name, ship, and passenger number. With this information you can easily request a copy of the original record.
Records in the series include:
Immigration Passes from 1879-1916
Register of Indian Immigrants from 1879-1916
Plantation Register 1879-1916
Repatriation Register 1881-1921
Death Register 1879-1927.
So far names starting with A-M are available to view online, and they continue to work on the rest of the list. The current list can be found at Girmit.org
With India looking to strengthen ties with Fiji, and those in Fiji starting to search for their Indian roots, this is a great resource. I look forward to searching through the records myself and finding family.