No need to book yet unless a mistake-fare appears. Mar-April is a low-ish season for which the "special" fares tend to appear in mid-to-late January.

SIN-PER is a short 4-hour hop very do-able in SQ or QF economy. With a 4-year old it may be better to look for a flight with several stops and keep him running up and down the corridors during each stop! I like OS via VIE which knocks 2 hours off the long Asian leg.

Don't know if there's any way to upgrade that long sector on eg LX/LH/OS with your BMI miles...

...or even buy-up eg just now MH has a £780 C-class fare between DBX and KUL see here

As you stumble exhausted into Perth ready for 12 hours sleep, your son will just be waking up ready for another energetic day.