Per Wiki: "In 1959, Qantas began the first jet service to Honolulu as a stop on its flights between Australia and California."
I'm not sure what you mean by "Jetport", but if the runways are long enough and able to support the aircraft weight then you could call it a jetport. Remember that there were no jetways back then, stairs were towed out to the aircraft and the passengers disembarked onto the tarmac. After all, Honolulu was a stopping off point for trans-pacific flights for a long time prior to the advent of jet service.
The 1959 Qantas flight was a promotional "round the world" flight. Regular jet service began out of HNL to US in 1960-1961 -- Pan Am and United. Honolulu has always been a busy airport, and for years had the longest runway, but that was a runway, not a jetway. The first jetways were additions completed in 1959. That is to say, in 1961 jet service was a very new thing. Flights were longer, had more stops.
And in 1961 HNL had old-style terminals. Their new jet-age terminal was not completed until August 1962.