How can I get from international terminal to Qantas cargo on Imperial Hwy, pick up my dog, and get back to a domestic terminal? Will I have to get a taxi?

Try google. There are tons of information.

I think the Beatles once said that you have to turn left at Greenland.

If the best advice you can get here on Fodors is to "Google it", seems like time to use Trip Advisor.

Why don't you just take a cab?

Yes, you will have to use a taxi. There are numerous "domestic" terminals at LAX. Which airline are you departing on?

You will need a taxi that will transport dogs.

Should be a $35 to $40 taxi ride, each way. What time of day is it?

Without luggage you could take the airport shuttle to the bus center off-airport (7 minutes)...wait 10 minutes for the Santa Monica #3 bus (10 min ride)...then take the Green Line train to Qantas (another 10 minute ride). You'd have to allow about an hour/90 mins for this $1.50 trip so it depends if you have time to kill. And no dogs allowed on the return so you'd have to find a taxi.

It is less than two miles. The taxi driver won't be happy. Not walkable, though, as I don't think there is a sidewalk in the tunnel on the PCH and even if there was a sidewalk it would be too nasty and scary.

Call the location and see if they have other options.

All in the same day?

Or is it an overnight?

Check out renting a car.

If you rent a car you'd have to be sure the car shuttle will take the dog to the airport. What kind of dog? big? small?