I'm no expert, but you should look to see written quotes before doing anything.
If you know of anyone in the business, you could ask them to have a look at them to see if they are reasonable!
But to be honest, it doesnt take much to rack up €1300 worth of damage to a car these days, especially as snowball says, if its a high end car!
As for claiming on your insurance, I would say thats what its there for! You need to calculate how much your no claims discount is worth to you vs the cost of the claim!