It may be possible to obtain Virginia insurance with some insurance companies if you already have the address of where you are going to be moving to and can provide it to the insurance company to start your policy. Some other insurance companies may want proof of VA residency or VA registration before starting up a policy though.
An easier way to transfer your auto insurance would be to find out if your current insurance carrier is licensed in both Virginia and Florida. If they are, you may be able to renew your insurance and thus continue your Florida policy until you complete your move to Virginia and then at that time have your insurance provider change over the policy from a Florida to a Virginia insurance policy.
For information on how to register your vehicle and obtain a Virginia driver's license once your move is complete, contact the VA Department of Motor Vehicles. To start comparison shopping for car insurance quotes for Virginia, click here.