He flew out of Auckland on Saturday night (NZT), on a Jetstar flight, arriving in the early hours of Saturday, local time. But his mission was in jeopardy when he realised his luggage - including all his surgical equipment - was not there.
"The only bit of communication when we arrived was a thing on the luggage conveyor belt - a little block of wood - coming around saying: 'If you have not got your luggage by now, contact your travel provider because it has been offloaded'."
The incident came after Rosser said he stressed to check-in staff the importance of getting his luggage on board.
"I explained that I was a surgeon going up to do eye surgery for the people who only get me once a year."
A Jetstar staffer told him there was a possibility one of his bags would not make it on to the flight because of weight issues.
"When I got here, neither of them had come up. So basically, I arrived with nothing."
He said he could not understand why passengers were ever boarded without their luggage.
Rosser has been giving eye care in the Cook Islands for the past 25 years and carried out more than 1000 cataract operations.
The team work on a semi-volunteer basis, donating their holidays and time and loss of earnings while in Rarotonga.
"We're the only trip that comes and operates on them and we only do it once a year.
"Some patients could be blind in two eyes, some patients are blind in one eye or some patients have just got two quite bad eyes and we'll do one of their eyes basically so they can see.
"It's a huge thing for the people because it gives them their sight."
Dr Rosser's luggage, as well as those of other affected passengers, was due to be sent to Rarotonga on Tuesday (local time).
Because the cataract surgeries were due to start tomorrow (NZT), that would have meant a minimum of 12 patients would have missed out on the surgery they needed.
However, in a statement from Jetstar late this afternoon, it was confirmed the airline was making a last minute bid to get Rosser's luggage on a flight due to arrive this evening.
"We apologise to Dr Rosser and our other customers whose baggage was offloaded on our Auckland-Rarotonga service over the weekend.
"Due to forecast weather conditions, the flight needed to carry additional fuel, which resulted in bags being offloaded to meet safety requirements."
Luggage belonging to other affected passengers will arrive in Rarotonga on Tuesday morning (local time).