The Australian Broadcasting Corp. reported that with 4 inches of rain having fallen already and winds whipping up to 75 mph, low-lying areas in the coastal community were being evacuated. The Sydney Morning Herald said the storm was about 105 miles north-northeast of Hedland at 8 a.m. local time.
About 2,000 houses and businesses were without electricity, the ABC said.
Les Hayter, a spokesman for the Department of Fire and Emergency Services, urged people in the region to take steps immediately to ensure their safety.
"Get into shelter, make sure you're in the strongest part of the house, make sure you have some food and water with you," he said.
"If you don't need to travel, don't travel. It's gone beyond that now, it's definitely don't travel.
"The roads are definitely closed, you will be fined and you will be really stupid to do it."
The West Australian reported Rusty was elevated to a Category 3 storm and the slow-moving cyclone could reach Category 4 level with winds topping 125 mph by Wednesday.
The newspaper said buildings were being boarded up with sandbags piled up to protect storefronts, and flights had been canceled.
Rains from Rusty caused flooding that killed at least one person and left another missing in Australia's Queensland state, authorities said.
Queensland, in the northeast part of the country, was on flood alert.
Weather officials said southeastern sections of the state could get up to 8 inches of rain in the next two days, the ABC said.
Forecasters said the path of the slow-moving cyclone was difficult to predict.
The drenching rains in Queensland caused a vehicle to sink in floodwaters in Kilcoy, north of Brisbane. Emergency workers said they removed the body of a man in his 60s from the vehicle.
Authorities searched for a woman who disappeared after she abandoned her car near a flooded causeway farther north in Pomona, authorities said.
A forecaster for the Australian weather bureau said about 3 inches of rain had fallen in the Toowoomba area since 9 a.m. Monday.
Residents of Gympie, along the banks of the Mary River 100 miles north of Brisbane, were being urged to prepare for flooding, with the river expected to crest at 52 1/2 feet Tuesday morning.
Water levels in the mid- and far-north coasts of New South Wales were beginning to drop, officials said, but 19,000 people remained isolated by flooding.