(CNN) -- It was supposed to be a dream trip: Two children and their parents on a yearlong family road trip around Australia.

But the dream turned to tragedy Wednesday when the parents apparently got into trouble while swimming off a remote beach in Western Australia, while their children, ages 10 and 12, were on shore.

The children watched as other beachgoers desperately tried to resuscitate their mother after her body drifted ashore, CNN's Australian affiliate ABC News reported.

The children had spotted their mother floating face-down in the water, ABC News said. Their father was also briefly seen floating face-down before disappearing under water, the broadcaster said.

Kathreen Ricketson, 41, is believed to have drowned, Western Australia police said.

The search continued Thursday for her husband, 48-year-old Robert Shugg, but there is little hope of finding him alive.

"His body hasn't been recovered," 1st Class Constable Richard Du Cloux of Exmouth police told CNN. "The search is still going on and will continue until all avenues have been exhausted."

The children have been reunited with family members, Du Cloux said.

The family was camping by Ningaloo Reef, a remote but beautiful spot about 45 kilometers (28 miles) south of Coral Bay, when disaster struck.

Ricketson, who described herself online as "mother.maker.wife.artist.writer.traveller. Adventuring with my family on year-long road trip around Australia," had been blogging about their trip.

Her last entry, posted Monday, reads: "We are bush camping at a station on Ningaloo reef, Western Australia. A dream come true -- is that totally corn ball?"

They had met another family there, Ricketson's blog said, and the children were enjoying playing together.

A photo of a beach at sunset posted to Instagram by Ricketson on Sunday was captioned: "Ningaloo beach for Robbie's birthday. Sweet."

"It's an extremely remote, rugged area," said Du Cloux. "People go camping there, (but) you've got to be fully self-sufficient, there's no amenities at all."

The alarm was raised by a fellow camper, who set off an emergency positioning beacon, Du Cloux said. The nearest police station, in Exmouth, is about 2½ hours away.

Efforts to find the body of the children's missing father are being led by the police and Department of Environment and Conservation officials, he said. An aerial search will resume at daylight Friday.

This kind of incident is thankfully unusual in the area, Du Cloux said.

The family set off on their road trip -- described by Ricketson as a "12 month family sabbatical to reconnect as a family and slow down our life" -- in early January.

The parents planned to home-school the children on the road and continue their online work, according to her blog. Ricketson ran a crafts and lifestyle website, Whip Up, as well as a children's activities website, Action Pack Magazine.

"We are deeply saddened by the tragic news of the sudden death of Whip Up founder, Kathreen Ricketson. Her partner Rob Shugg is still missing at Coral Bay, Western Australia. Their two gorgeous, beloved children, to whom we send our love, are with relatives," a post by a contributor to the Whip Up site said Thursday.

"This was their adventure of a lifetime and it has come to an end in the worst imaginable way."