The jobless rate did tick up to 4.2 percent, from 4.1 percent in March, but only because more people were looking for work. The participation rate climbed 0.2 percentage points to a record high of 65.4 percent as more women joined the labor force.
"There's absolutely no sign of any weakness in the labor market," said Brian Redican, a senior economist at Macquarie.
The rise in the participation rate meant that strong demand for labor was being met with increased supply, so it was not directly inflationary, he added.
"Still, more jobs means more household income and that should support economic growth. So in that sense, there's no pressure valve here for the RBA and its concerns about inflation."
The Reserve Bank of Australia (RBA) kept interest rates at a 12-year high of 7.25 percent at its monthly policy meeting this week and warned that it might yet have to tighten further if domestic demand did not slow as expected.
Analysts noted that employment does tend to lag big turns in the economy and other indicators were signaling a slowdown.
Consumers, shaken by rising mortgage and living costs, have cut back spending on retail goods and autos, while the housing market has cooled and business activity softened.
Yet while firms were worried about the outlook there was no sign as yet of them firing people. Indeed, most consider a lack of suitable labor as more of a constraint than weak demand.
In the year to April some 311,400 new jobs were created, a blistering result for an economy with a potential labor force of just 11.1 million. Growth in the past year has been greatest in utilities, construction, manufacturing, education and health.
While the mining industry has been booming, it is a capital-intensive business and jobs growth has been flat. The sector accounts for just 1.3 percent of all employed, compared to 11 percent for both manufacturing and health.
Such speedy growth has stoked concerns of a wages break-out, particularly as core inflation hit a 17-year peak of 4.2 percent in the first quarter.
RBA Governor Glenn Stevens was fretting about it this week. "Should demand not slow as expected or should expectations of high ongoing inflation begin to affect wage and price setting, that outlook would need to be reviewed," he said.
Up to now broad measures of wages have been remarkably steady, showing growth of around 4.0 percent a year.
However, Australia's unions, emboldened by the election of the left-leaning Labor Party to government, have been agitating for much bigger pay raises.
Teachers in the state of Victoria this week won an effective pay increase of 15 percent for this year.
"The Victorian teachers pay deal is likely to be a template for public sector cost of living adjustments, and the risk is that these flow over to the rest of the economy," said Matthew Johnson, a senior economist at ICAP.
He worried that non-unionized sectors would be forced to follow to prevent skilled labor from bleeding away.
"With 4 percent unemployment, this dynamic could be swift," said Johnson. "There is a very real risk that high inflation will become embedded in wage settlements, which would mean interest rates have to rise again."