Pianos are an extremely delicate and 'unforgiving' item to move and MUST be done professionally if the condition of your instrument matters too you - and your own health! We can refer you to the proper professionals to get it done safely, and securely.
Generally as a large and permanent item of 'furniture-like' significance in your home or educational institution, the piano of medium value may not require specified insurance. Whereas in the professional/ concert/ public setting where the instrument may be worth many $1000's it will require specific insurance cover. Check with your Insurance professional.
For shifting, professional carriers will have limited liability insurance. If you are concerns ask your carrier and insurer.