Qantas is in the AA terminal now, #4, you can walk there, 15 min walk (rent a cart for you bags), walk on upper level roadway, you can get some good views of Airplanes, or you can take any lower level shulle bus B,C, ect since SW is terminal one, they will all to to terminal 4. I do the CX and Southwest conections before, and had no problem, in fact when my CX flight was late 3 hours and I missed the Southwest flight, CX rebooked and paid the higher fare for the flight, but Southwest will not do this for CX.

As for what to do,some cheap trips you can take Free bus G from lower level to the GREEN line rail line station from there you have a few choices:

(A) Take Santa Monica bus line 3 (runs every 10 min, 75 cents) to In and Out Burger, or futher north to Santa Monica (about 40min), it also passes Marina Delrey area. The #3, some also go as far as Montana Ave, kind nice street of cafes and shops.

or
(B) catch the GREEN LINE to BLUE LINE north into Downtown LA, stop at Grand Central Market for food, visit Little Tokyo ect.