Firyice, as you already knew, Singapore and Los Angeles are the two international destinations on the A380 for Australian based crew.
The trips though are mainly 3 day trips for SIN (SYD/MEL-SIN-SYD/MEL) and 4 or 5 day trips to LAX (SYD/MEL-LAX-SYD/MEL).
However some patterns are constructed with multiple layovers in SIN separated by a slip in MEL or SYD, ie SYD-SIN-MEL-SIN-SYD.
Expected layovers in SIN are 24 or 36hrs and in LAX 40 or 64hrs.