Verbatim reports are permitted, the question is whether other reporting is.
A newspaper could run a verbatim report and would have the same protection as Hansard, but if they want to address the question in their own language, paraphrase, edit or in general write their own story, then they may not be protected.
The absolute privilege of parliamentary proceedings is established by the Bill of Rights (1689), and it extends to verbatim reports. Because Hansard consists solely of verbatim reports, it has absolute privilege entire.
Whether a report of parliamentary proceedings has qualified privilege if it's not verbatim (qualified, because it's only privileged if it's a fair and accurate report) is unclear - court reports have exactly that qualified privilege, and it would make sense for parliamentary reports to do so.
Because that privilege exists in common law (ie not defined by statute) and because the question has never been tested in court, no-one can know for certain whether parliamentary reports have QP - it would be expensive to find out.