An Adelaide mother reported missing in the wake of the New Zealand volcanic eruption is in hospital with severe burns — but there is still no word on her husband and daughter.

Key points: Gavin and Lisa Dallow and her daughter Zoe Hosking were on a cruise in New Zealand

Gavin and Lisa Dallow and her daughter Zoe Hosking were on a cruise in New Zealand Mr Dallow's father Brian said the family were on the island

Mr Dallow's father Brian said the family were on the island Zoe Hosking's school has released a statement confirming the family is missing

Lisa Dallow, 48, was on a two-week cruise with her husband Gavin Dallow, 53, and her daughter Zoe Hosking, 15, when the volcano erupted on White Island on Monday.

A family spokesman confirmed Ms Dallow had been found alive but said she had severe burns and is in a hospital in Hamilton.

Her husband and daughter are still considered missing.

In a statement provided a short time ago, the Dallow family said it was praying for the safe return of all of its loved ones.

"We feel for all the families who are going through the same frustration and fear for loved ones as we are," the family said.

"All we can do is pray for their safe return.

"Our thoughts also go out to the emergency workers who have done so much for the injured and ask that their safety is paramount."

The family said it was receiving support from the Department of Foreign Affairs and Trade (DFAT), the Red Cross and cruise company Royal Caribbean.

Forty-seven tourists — many of them from the Ovation of the Seas cruise ship — and guides were on the tiny island when the eruption occurred.

Brisbane woman Julie Richards and her daughter, Jessica, are also missing, while experienced tour guide Hayden Marshall-Inman is the first victim of the disaster to be publicly named.

Three Australians are believed to be among five people confirmed dead.

Speaking from his Adelaide home, Mr Dallow's father Brian said the trio had been on a daytrip to White Island.

"We do know they were on the island. That is definite," he said earlier.

"At the moment, we think they might be in hospital. We're not sure. We really don't know anything."

Zoe Hosking is a Year 9 student at Adelaide's St Aloysius College (SAC) which this morning issued a statement confirming the family was missing.

Lisa Dallow and Zoe Hosking. ( Supplied )

"Our thoughts and prayers are with Zoe and her family," principal Paddy McEvoy said.

"The SAC chapel is open and school counsellors are on hand to support students.

"We know that you share our sadness at this time. We turn to our loving God to give us strength and courage in the days ahead."

Mr and Ms Dallow were married in 2017.

Ms Dallow is an engineer at Santos, while Mr Dallow runs his own legal firm.

Rotary community hoping for the best

Both are heavily involved in Rotary clubs in South Australia.

Rotary District Governor Jane Owens said the news had hit hard for everyone in Rotary.

"I'm devastated, I know Gavin and Lisa very, very well, and Zoe," she said.

"I'm just hoping and praying for the best."

The eruption sent smoke, ash, steam and rock 12,000 feet into the sky. ( Facebook: Bay of Plenty Civil Defence )

She said both held senior positions in her district and were active members of the Rotary community.

"In fact, Lisa and Gavin actually met through Rotary and were married by a Rotarian in Lisa's club," she said.

"They've got a lot of community in them, and are very much a part of the Rotary family.

"Our members are very important to us and we will take every action to help families and communities recover from this disaster."

Rotary Adelaide posted on Facebook that it was "praying and hoping for better news".

"Gavin is a longstanding member of the Prospect Rotary club and of course [his] wife Lisa is a valued member of our club," it said.

"Together with daughter Zoe, they are very much in our thoughts."

Sleepless night for family

Brian Dallow said he "didn't sleep too much" last night.

Adelaide man Brian Dallow confirmed his son Gavin was missing. ( ABC News )

"We picked it up on the six o'clock news last night and we were switching around news channels from there on," he said.

"Whether they got off [the island] or what happened, we don't know.

"This is the worst — I mean if we knew something about it, it would be better than this waiting I can tell you at the moment."

He said his son was planning to fly to Melbourne for Christmas following the New Zealand holiday.

"He's a lines umpire in the tennis so he was flying back here for the tennis and then he was flying back to Melbourne for the [Australian] Open, so all that is up in the air now," he said.