Haji, n. A Haji is a Muslim who has made the pilgrimage to Mecca, and this sense of the term in English usage dates back to the early-seventeenth century. But in 2005 in U. S. military slang Haji acquired the sense of any native of a Muslim country.
Although the word usually has one -j- in this transferred sense, it is correctly spelled with two (Hajji), so I think this should read: “A Hajji is a Muslim who has made the pilgrimage to Mecca (the Hajj)...” Also, there should be no hyphen after “early.”