Yes - insurance is certainly important to protect all your goods, but check your content insurance if you have as you may already be covered. Before spending up with our removalists, something made me check with our contents insurance company NRMA. Our contents policy covered our goods if packed onto or unloaded off the truck in a driveway. If loaded on the road, that is no longer on your property so your contents are not covered ......... but of course, who is to say that your vase didn't get broken on the front lawn! ;0)
The policy also covered the goods in transit as well.
So many people just pay what they have to to the removalist company, so it pays to check with your contents insurance company first!