I would just stay at an airport hotel the first night and save a little $$$ for the cost of a rental car and possibly parking. Wake up the next morning, have breakfast, pick up the car, and by then you will miss most of rush hour. With more than one passenger, you can take the carpool lanes and save even more time. If you stay at the Renaissance or Four Points, you can pretty much walk across the street to Budget and Hertz.

I agree that the best route from LAX to LAS is the 105 E to the 605 N to the 210 E to the 15 the rest of the way. This can be done in about four hours without stopping.