No, you are not eligible, because your main destination is clearly Korea. In fact your itinerary is specifically called out on the official site:
If you visit only Korea from the country of departure(e.g.,Australia) and return to the country of departure(e.g.,Australia), you must get a visa.
The fact that you happen to be transiting via Singapore and Vietnam on your way to Korea is irrelevant.
Now there is one potential exception. This itinerary is listed on the site as allowed:
Home Country → Korea → Third Country → Australia / [Possible]
Since your home country is Vietnam and you are flying from Vietnam to Korea, you could maybe argue that you are not "transiting" Vietnam, but departing from it. But since this is a visa-free program, and you would also need to convince the airline in Vietnam to let you board, this seems risky and it would be much safer to get a regular Korean visa. As an Australian PR, the visa is very likely to be granted.