TR operated both SIN-PER and SIN-DRW for a period, but dropped SIN-DRW a while back. I belive it was something to do with DRW not wanting to upgrade facilities, but as docjames say landing fees may also have been an issue.
When TT first started operations ex-MEL it was possible to buy MEL-DRW-SIN on a single ticket. This was technically an interline fare, as TR and TT are seperate carriers (from registration point of view).
Basicly you took TT on the MEL-DRW sector, collected bags, and then checked in again for DRW-SIN on TR. (and the same on the return). The flight times involved an overnight, and a 2.5 hour layover in Darwin, although some of this time was wasted standing in line. The one time I did this (early 2008) I found it to be fairly unpleasant.
This setup no longer exists.
There is currently no interline tickeing between TR and TT. However TR do offer some through fares to TR destinations in Asia ex-PER (eg. PER-SIN-BKK). These fares are on 2 TR flights and AFAIK they involve 'entering Singapore', collecting your bags, and then checking in for the second flight.
If you wanted to travel MEL-PER-SIN you would need two tickets (one on TR and one on TT).
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Jetstar (JQ) now offer a similar arrangement for the MEL-DRW-SIN as what I described above for TT and TR. Basicly you take JQ domestic to DRW and then recheck for the JQ international sector DRW-SIN.
Depening on your final destination other cheap options may include AirAsiaX via KUL or discounted fares on full service carriers.
