Welcome to the Forum...
Depending where in Alabama you're coming from. You could take I-20 west into TX where it merges into I-10 then continue westbound to Quartzsite, AZ then take US95 up through Parker & Lake Havasu, AZ, to I-40/US95 then continue on to Las Vegas on US95.
If you have some time to spare, you might want to spend a couple of days or so in Quartzsite, it's an interesting place where a lot of Snowbirds congregate during the winter months.
Best of luck and safe travels...