"Our future lies around the Pacific Rim," said Dunkerley, who as the airline's president and CEO has overseen big growth in recent years. "We're about four times larger than we were, say, six or seven years ago."
Analysts agree that Hawaiian has had quite a run under Dunkerly. It was the highest-rated among U.S. carriers for on-time arrivals last year, landing 91.1 percent of its flights as scheduled. That's well above the industry average of 81.4 percent, according to the Department of Transportation.
Financially, Hawaiian Airlines is coming off one of its most profitable years ever, having earned a net income of more than $244 million. That's up 33 percent from the prior year.
Yet despite its momentum, some analysts remain skeptical of Hawaiian's growth potential. Their biggest concerns include the added complexities that come with adding new destinations in Asia or East Coast of the U.S.
"I worry a little bit that they are beginning to get a little bit too aggressive," said Scott Hamilton, managing director of Leeham Company, an aviation consulting firm. "They have very ambitious long-haul expansion plans, which of course is all well and good, but you need very expensive airplanes to do that. So I am just a little cautious as to what they have on the plate right now."
The new airplanes include the Airbus A321, whose smaller size will make it a better fit for some markets along the Pacific Coast, where Hawaiian currently uses larger planes. Those larger planes can then be better positioned to serve other markets — the question is, which ones?
Dunkerley is careful not to mention specific cities, though he's clearly focused on markets in the Pacific Rim. "That's where we see demand for the Hawaiian vacation," he told CNBC during an interview at the company's hub in Honolulu.
The challenge for Hawaiian is expanding and adding new routes in an industry where a decade of mergers has created larger and stronger competitors that dominate some of the largest U.S. cities.
For example, Hawaiian does not fly directly to Chicago—the home of United Airlines, which has long had direct flights into Hawaii. It's also at the mercy of jet fuel prices, which could send the industry into a slump if they suddenly surge.
"When you get long-haul airplanes you have to carry a lot of fuel. There is a lot of expense," Hamilton said.
"If you have to cut back it is hard enough for somebody like an American Airlines with a global network to reposition these wide-body airplanes," he said. "Hawaiian Airlines, with its very unique route system, if they have to start to have to cut back, where do they reposition those Airbuses?"
Despite those challenges, Hawaiian doesn't yet have M&A activity in its sites.
"We think we can continue to grow," Dunkerley said. "I think what's important for our business is that we run the best possible airline that we possibly can as an independent airline."
(Phil LeBeau - CNBC / Yahoo Business News)