Get a 2nd opinion. Dealers are too quick to assume the problem without taking time to properly diagnose. Just went through the same thing with my Honda. It wasn't blowing cold anymore so I brought it to the dealer. They said it had a leak and the system was empty which in turn damaged the compressor and condenser. The whole system needed replacing at $2k.
I thought it was odd that they could determine that without doing a leak test or anything. Brought it to a friend who tried to charge the system but couldn't because it was full, no leak. Five minutes with an electrical tester found a faulty relay. $29
The dealer hasn't finished hearing from me yet.