Go and have a look at www.southwest.com.

On Sunday 13 June there are LAX-LAS flights at 800a, 915a, 1025a, 1120a, and 1200p. The one-way fare is $161, which is a bit costly, but you're booking very close to the travel day so it can't be helped.

If your longhaul flight is due into LAX at 700am I would book the 1025a departure on Southwest. You will have to get through Customs at LAX, which can take forever, and then transfer terminals with all your baggage, checking your big bags with Southwest no later than 45 minutes before departure. Southwest goes from Terminal 1 at LAX; there's a free shuttle bus.

You can check in online with Southwest and print off your own boarding passes up to 24 hours before departure, so I should think you could do it before you leave Brisbane and bring them with you. If you don't manage that, just use the touch-screen kiosks in the lobby of Terminal 1 to check in. If you miss the 1025a, or miss the baggage deadline, just present yourself at the Southwest ticket counter at Terminal 1 and explain yourself, and they'll put you on the next flight with space. There are plenty of them.

Southwest is a little different in that there are no assigned seats, just a boarding order ("A," "B," and "C"-grade boarding passes)... but if you check in 24 hours in advance you'll have A-grade passes.

It's very easy to fly Southwest, and it's a quick hop up to Vegas -- less than one hour in the air.