Taxpayers have funded $48.8 million in capital costs for the facility near Toowoomba, which has replaced quarantine hotels.
It's understood the government is spending even more to lease from the Wagner Group and run the facility.
Health Minister Yvette D'Ath says the full price tag can't be revealed because it's commercial-in-confidence.
"These are the figures that we have agreed to release and Wagners have agreed to release," she told reporters on Thursday.
The Liberal National Party has written to Auditor-General Brendan Worrall asking him to investigate the project.
LNP finance spokesman Jarrod Bleijie said taxpayers deserve to know how much was spent and if the procurement process delivered the best value for money.
He's also asked Mr Worrall to probe whether keeping some of the cost secret was in line with government disclosure policy.
"Too many questions remain unanswered regarding the use of taxpayer funds at the Wellcamp quarantine facility," Mr Bleijie said in a statement.
The health minister said the Wellcamp tender process was run by the Department of State Development, Infrastructure, Local Government and Planning.
She said journalists should refer to Deputy Premier Steven Miles about the processes and refused to say whether Queensland Health was involved.
The government complied with a whole range of procurement processes, the minister said, telling journalists to ask Mr Miles about the Wellcamp tender before making "accusations".
"Certainly put those questions and get that information, before we go down that rabbit hole," Ms D'Ath said.
The state and Commonwealth are also building another quarantine facility at Pinkenba near Brisbane Airport.
The second facility was unlikely to open before April, the minister said, and she doubted if it would ever open, which was part of the reason why the state went it alone.
"We've waited for two years for them to get off their backsides and help us with hotel quarantine and manage isolation, and they've done nothing," Ms D'Ath said.
The minister said it was inexplicable the Morrison government hadn't partnered the state on Wellcamp, particularly after it had done so with the Northern Territory government on its Howard Springs camp.
The minister also blamed virus outbreaks in the state's hotel quarantine program and subsequent lockdowns on the Commonwealth.
"It could have been avoided if we had had these purpose built facilities and the Commonwealth had partnered with us," Ms D'Ath added.
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