If your car is still registered with your state during the time which your license is suspended or revoked, due to the DUI, then your state most likely will require you to keep at least the state's minimum auto insurance on the car.

If you plan on turning in your plates and not having registration on your vehicle during the time that you are unable to drive, and thus keeping the car in the garage, then likely you can take insurance off of the vehicle. Some states will allow you to suspend your registration due to the car being inoperable, being out of the state due to military orders, etc so you may see if they will allow to suspend your registration for your situation and then reinstate it once you are able to reinstate your license and insurance.

Since state laws differ check with your state's Department of Motor Vehicles to see what is allowable in the state that you reside in. Just remember that if there is no insurance or registration on the vehicle the car should not be driven. So if you plan to allow others to drive you around in your vehicle during the time your license is not valid you will need to keep the car registered and insured.

Also, if you have financed the car and have not yet paid it off, then your lien holder will require you to keep insurance on the vehicle, to protect their asset, even if you do not plan to drive it during your 1 year license suspension.