For Krisflyer, I suggest having a read of this PH page.
Singapore airline free stopover is for return redemptions. If only one way, you need to pay USD100 per passenger per stop over.
2 Adults + 1 child (considered as adult for redemption) cost 102k (econ) 165.75k (business) return flights. (half for one-way)
Surcharge & taxes total to: 893.72 (2 adults) + 371.26 (child) = ~$1265 (return).
You will need to buy infant tickets, which cost approx 10% of what an adult ticket cost in cash. So costs depend on which class you are flying.
Redeem for the 3 of you and then ring Singapore Airlines to buy ticket for bub. Agent would attach bub booking to one of the adults on your redemption booking.
2 Adults + 1 child (considered as adult for redemption) cost 210k (econ), 390k (business) return flights. (half for one-way)
Surcharge & taxes total to: = ~$629 (return).
With Qantas and Velocity, infant flies for free.
Other than the comparison of out of pocket cost, ultimately it depends on availability of award seats.
To search Singapore Airlines -> Singaporeairlines.com-> select redeem and search as you would a normal revenue flight.
To search Qantas ->qantas.com-> Select Classic Rewards and search as you would a normal revenue flight.