Air Asia does not interline with anybody. So if you fly them into SIN, you'll definitely have to go through Immigration then Baggage Claim/Customs, and back to Departures to check-in with OZ or your selected onward carrier. Singapore Immigration and follow-on is pretty efficient, so generally a couple of hours' scheduled arrival to scheduled departure is sufficient. However, Air Asia is not necessarily punctual and therein lies the potential problem. What happens if there is a delay of one hour, two hours, four hours....?

Old Asia hands tend to never schedule an Air Asia regional flight followed immediately by a long-haul international, without an intervening day or night between the two. The gamble is just too great.

With mainline airlines that interline (ie. OZ and SQ), you should be able to avoid passing through Singapore Immigration if that is what you prefer. Boarding passes not issued in Kuching can be handled at airside transfer desks in SIN. If you ever have need of a Transit Hotel airside, SIN's are quite decent, quiet and very clean with everything you need for privacy and a good sleep that a lounge can't provide.