The family said they hoped that the inquest would reveal what happened while Ms Dhu served a brief jail sentence for unpaid fines.
The Deaths in Custody Watch Committee has been rallying for nationwide support for a coronial inquest for almost a year.
Marc Newhouse from the watch committee said the campaign had been central to the resulting inquest.
" There is no doubt that the campaign not only in WA but around the country, but also the families meeting with the premier which happened about a month ago in Port Hedland, were all significant factors in getting this Inquest to happen a the earliest possible time," he said.
The Coroner's office was unable to confirm the date of the inquest's commencement, but said an announcement would be made soon.
Mr Newhouse said it was essential it occurred soon. "It's in humane," he said. "It needs to be done as soon as possible [so] it and whatever mistakes or errors were made can be corrected to prevent further deaths."
It is believed that the inquest will continue for four weeks, with the findings made public around a month later.
Rallies to commemorate the anniversary for Ms Dhu's death on 4 August are scheduled across the country.
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