You very much can! Los Angeles is the second-largest city in the U.S. and the largest on the west coast and in the state of California. It is a major population center as well as the largest transportation hub west of Texas, so finding auto transport from Los Angeles should not be difficult.
Las Vegas, too, is a major population center, this time in Nevada. Auto transport carriers often pass through Las Vegas on east-west routes and many of them either start in or end up in Los Angeles. Finding a carrier at a great rate to ship from Los Angeles to Las Vegas will be a piece of cake!