Yes, you should be able to purchase and insure a car in Las Vegas, Nevada with a Florida driver's license but if you have moved to Nevada and plan on staying as a resident of this state then you will need to obtain a NV driver's license.

According to the NV DMV, new Nevada residents must obtain their driver license within 30 days and if you brought a car with you to NV you would need to obtain vehicle registration within 60 days. The fine for failing to register your vehicle is $250-$500.

Insurance must be issued by a Nevada-licensed carrier for a motor vehicle registered in state. Out of state insurance is not accepted. Minimum liability insurance requirement is $15,000/$30,000/$10,000. You must keep a Nevada Evidence of Insurance card in your vehicle at all times and present it to law enforcement upon request. 

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