"We would like to thank our family for their love and support during this difficult time," it said.
"We would also like to thank the amazing staff at the QCH who have cared for our boy, and the emergency services personnel who were there for us in those first few critical hours.
"We sincerely appreciate the thoughts, prayers and well wishes that have been publicly expressed for our family.
"Our son is doing well and we anticipate a full recovery. As we continue to focus on his recovery, we ask that you continue to respect our privacy."
The dingo snatched the boy from the camper trailer about 12.30am on Friday and was heading towards bushland when the toddler's father heard his son's cries.
A Department of Environment and Science spokesman said on Tuesday it was believed the dingo had entered the family's camper trailer, not a campervan as previously reported.
Paramedics said the father chased the dingo, grabbed his son from the animal's jaws while he was surrounded by a pack, before chasing the remaining animals away.
The boy was flown to Hervey Bay Hospital with a fractured skull and multiple puncture wounds to his neck and skull, before being transferred to the Queensland Children's Hospital.
The toddler had surgery on Friday afternoon and was released with his family, who are from Brisbane, about lunchtime on Tuesday, according to a QCH spokesman.
Criticism of the state government's existing approach to dingoes on the island prompted an urgent review.
Others demanded a dingo cull but there was no data on the number of native dogs in the township.
The Butchulla Aboriginal Corporation - the island's native title holders - issued a statement on Friday saying the attacks could have been avoided.
"To the family affected by this tragedy, it is our deep regret that this has happened, and we send our sympathies," a spokesman said.
"It is our regret, because the BAC has been kept at arm’s length from the government’s dingo conservation and risk management strategy on K’gari [the traditional name for Fraser Island] and its associated awareness campaigns, since gaining our native title rights in 2014.
"It is time that people are more accountable for the actions - Wongaris [dingoes] should not be
sacrificed for human error or inciting interaction."
One fed-up local said Fraser Island tourists could be heard boasting about how they ran over or shot a dingo and were often seen luring the deadly animals with food to snap a selfie.
Long-term resident Hannah Robinson said some visitors didn't realise they shouldn't camp in unfenced areas with children under 12 and called for more information to be made available.
Ms Robinson, who owns Drop Bear Adventures on Fraser Island, said there was not enough education about how to be dingo-safe on the island, and more attacks were bound to happen.
Two French tourists were flown to hospital after an encounter last month, which led to two dingoes being euthanised.
A nine-year-old boy suffered face, arm and leg bites and his mother was bitten on the leg after trying to flee from a pack of dingoes in January.
Toby Crockford is a breaking news reporter at the Brisbane Times