Dawson said firearms were also found at the scene.
There was no ongoing threat to public safety, police said.
Dawson described the deaths as a tragedy.
Authorities were called to the scene at 05:15 local time (21:15 GMT on Thursday) after receiving a phone call from a "male person", Mr Dawson said.
Osmington is a collection of a few streets, farms, horse studs, vacation accommodation and vineyards supplying the premium winemaking district known as Margaret River.
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The ages of the children and adults have not been revealed. We are trying to locate other members of the family and friends.
The shooting is believed to have been a murder-suicide but this is yet to be confirmed.
"This devastating tragedy will no doubt have a lasting impact on the families concerned, the whole community".
The commissioner said the police chaplain had been called to attend the scene of the tragedy to support the emergency services. Two adults lay on the outside, and another adult and four children inside the building.
"This will be a very large scale and detailed investigation".
A local resident who did not want to be named said he understood the property belonged to the grandparents.