By booking separate tickets, you are taking on a number of risks, most importantly that it there is a problem with your PDX-LAX flight and you miss boarding for your Qantas flight, you are a no-show and Qantas has no legal obligations to honor your ticket or rebook you, although they may put you on standby on another flight as a customer service gesture.
In the event that you are not able to interline your bags, you will need sufficient time between the flights to reclaim your bags, transfer terminals, re-check your bags, and clear TSA security. I would allot four hours for peace of mind.
In general, U.S. airlines are much less willing to interline now than they were even five years ago. Alaska will still do this with partners, of which Qantas may be counted, but you will need an agent who is willing and able to do it on separate tickets.
Check in for both flights before you leave home. Go to the counter at PDX early, with a printout of your Qantas itinerary. If it is not too busy and you get an amenable agent, you may be able to get your bags checked through to the final destination, which would be ideal.
If your bags are interlined to Australia, then your experience at LAX will be very straihtforward. You will most likely arrive at Terminal 6. Your bags will be transferred automatically by the airline, and you will not need to pay any additional fees. You can then take the airside underground passageway from T6 to T4, then take the pedestrian walkway to the Tom Bradley International Terminal, where Qantas flights depart from. You will not need to re-clear security.
While there is a shuttle bus, it goes counterclockwise around the terminals, which is the opposite direction you need to go, and is subject to epic traffic jams going through the airport loop.
If Alaska will not interline your bags to Qantas things will be more complicated. After you arrive at Terminal 6, you will need to exit the secure area and collect your bags at the baggage claim area. You can then walk on the arrivals level from Terminal 6 back to TBIT.
You will need to check the bags with Qantas; their counters are in Aisle B. If any Qantas baggage fees apply, you will pay them at this time. You must then re-clear TSA security at TBIT to get to your departure gate.