For the first 6 weeks, sailors cannot have their cars, they aren't even allowed to leave base. If they have a relatively short A school (14 weeks or less), it's not really worth it to bother with shipping the car. Once they get their permanant duty station, if it is in the US, sailors may be allowed to drive their own vehicle to the new duty station. However, if they are on sea duty, that means parking the car in a long-term storage lot, where the salt air tends to do a lot of damage.
You can garage the car, once you do, you can inform your insurance company that the car is garaged. Depending on YOUR state law and loan/lease rules, you may be able to drop the insurance on it, or reduce coverage to special low rates for unused cars. Once your daughter is settled in somewhere permanent, you can both make a decision on what to do about the car.
This needs to be an informed decision for you and your sailor.