Are you sure it is the water pump, or the 'death pipe' that runs from the pump to the block. This is an approx 1" diameter plastic pipe 8 or 9" long, that degrades through heat cycles and age. When one of these pop with the engine running the car can dump all it's coolant very quickly, as the pump is right next to this pipe.
When mine was having it's injectors and flaps sorted, it was noted that my pipe was leaking a little bit, so I caught mine just in time.
As said earlier in this thread, the Y piece is also a common failure point (happened on mine too).
Mine also had a heater matrix pipe break too.
Unfortunately it is a result of plastic pipes, they seem to have a certain life span. It's also very common for one to crack/break after having a service and the pipes get disturbed. Since they are brittle it's quite easy to crack one sometimes, then you have a small leak which can be hard to track down. These pipes are down to production costs, it's much cheaper and easier to make a plastic funny shaped pipe, than a metal version.
The price you've been quoted is very high though. The rear coolant pipe is in a pretty inaccessible place(right at the back of the engine between the block and the firewall). I would recommend you speak to some other garages, possibly audi specialists who have done this job before. It might save you some money in term of labour or parts.
