If your laptop bag is not like an "overnight bag" then it can be considered a personal item.

Your basic baggage allowance depends upon you ticketed class and route.

(http://www.qantas.com.au/travel/airl...al/en#domestic)

Check your ticket ... does it indicate x Pieces or y Kg?

As an Emerald frequent flyer you can check in one additional bag for free in addition to your ticketed baggage allowance if it states "Piece" or "PC". If your ticket mentions a weight allowance, you can check in an extra 20kgs over and above the allowance indicated.