
I bought my car below market price (overseas student needing to sell before they went back home) and had a similar issue. I'm with JustCar Insurance and my vehicle is insured for around $6K more than what the transfer paper work says. This way I am safe and know that I could get a comparable car if something happened to mine.
Naturally the insurance company wanted to inspect the vehicle and wanted to know how I managed to get it so cheap, but once they did the inspection and heard my story they were satisfied and put the cover up to the appropriate level.