SYDNEY—From the vast mining pits that dot Australia’s arid northwest to the multimillion-dollar luxury homes with views across Sydney Harbour, economists are seeing red flags that point to a looming economic slump.

Thousands of kilometers away, China is providing another cause for concern. The country buys roughly a quarter of resource-rich Australia’s exports. But its slowing economy translates into less construction of skyscrapers, bridges and railways—hurting demand for raw materials like iron ore.

The...