In Australia, Amazon is still finding its way

* Reuters orders three Santa hats, one makes it on time

* Australia is the world's most spread out developed country

* Geography undercuts Amazon's competitive advantage in Australia

By Tom Westbrook and Byron Kaye

SYDNEY, Feb 5 (Reuters) - When Kiri Pomery ordered a red Santa Claus hat from Amazon.com Inc's new Australian operation, the estimated delivery time to her address in outback Western Australia seemed too good to be true.

It was.

Several weeks after the end of Amazon's Jan. 10 delivery window and a month after Christmas, the manager of the Ora Banda Historical Inn had still had not received her package.

"Generally it is pretty reliable," said Pomery, referring to the nearest post office, a 45-minute drive away in the gold mining town of Kalgoorlie, where she collects her mail. "I think we have had one thing in the last four years that we have had to go looking for."

On the other side of the country, at a pub she manages with her husband, Lester, in the spinifex plains of far western Queensland state, Valerie Cain got her Santa hat in time to wrap it as a Christmas gift for her six-month-old grandson Oscar. The hat arrived just two days into Amazon's 20-day estimated delivery window.

A third parcel bound for the tiny township of Yuendumu, in Central Australia's Western Desert, arrived nine days after Amazon's delivery window.

Reuters ordered the hats in December to check Amazon Australia's shipping estimates. And the experiences of three of the company's first customers reflect what analysts see as the main challenge to capitalising on a lack of serious online competition and winning over the world's 12th-largest economy: its geography.

Australia has the developed world's most spread-out population, with 24 million people on an island roughly the size of the mainland United States. Yet there is little inland transport infrastructure, making it hard for Amazon to live up to its promise of reliable shipping times.

Amazon can generally reach customers in far-flung parts of North America and Asia quickly by using income from its subscription service, Prime, to bankroll its own delivery vehicles. The company has said it plans to offer Prime in Australia sometime in 2018.

"Retailers that have been here and have had an online offer for the last 10 years are all struggling," said Shanaka Jayasinghe, a manager at logistics consultant GRA Supply Chain Pty Ltd.

If a company is trying to ship to all of Australia, "offering same day or next day, it's a challenge in our market," Jayasinghe added, referring to shipping times.