Cleo Smith's parents release statement after 4-year-old miraculously found

A police officer carries rescued girl Cleo Smith in Carnarvon. Photo / WA Police

The parents of Cleo Smith have thanked all those who were involved in her dramatic rescue for making their family "whole again".

The four-year-old was allegedly taken from the family tent while camping at Quobba Blowholes, 75km north of Carnarvon in Western Australia, on October 16 and was missing for 18 days.

In a statement released on Friday night, Ellie Smith and Jake Gliddon said: "In particular, we would like to thank WA Police, all those involved in the initial search, the Carnarvon community, local businesses and, of course, our family and friends.

"We are humbled by the love and support that we have received from not only our local community but the whole of Western Australia and across the country.

"We are so thankful that our little girl is back within our arms and our family is whole again. As we try to get on with our lives, we ask that you respect our privacy."

Cleo Smith's parents Ellie Smith and Jake Gliddon. Photo / Supplied

Cleo was rescued from a locked house in Carnarvon – not far from her family home – just before 1am on Wednesday after detectives burst in.

Terence Darrell Kelly, 36, had been arrested about an hour earlier and has since been charged with two offences including one count of forcibly taking a child aged under 16.

During his court appearance on Thursday, Kelly verbally lashed out at the media.

He was remanded in custody to face court again on December 6.

Barefoot and wearing a long-sleeved white shirt, Kelly was shackled as special operations group officers escorted him onto a plane at Carnarvon Airport on Friday morning.

A police officer carries rescued girl Cleo Smith in Carnarvon. Photo / WA Police

They arrived at Jandakot Airport, in Perth's south, a couple of hours later and Kelly was whisked away in a highly secured van to a maximum-security prison.

Cleo's disappearance sparked a massive land, air and sea search, and hit headlines around the world.

A $1 million reward was offered that police said will likely not be claimed.

West Australian Premier Mark McGowan visited the family's home on Thursday, holding two teddies — one for Cleo and the other for her younger sister Isla.

"Cleo was a delightful little girl, who was playing in the backyard and I gave her the two teddies, which we named," he said.

McGowan said they named the teddies Cameron and Rod after the detective who rescued her and the lead investigator on the case, but he was unsure whether those names would stick.

"Cleo didn't seem too enamoured with those names," the Premier joked with reporters.