Hi Yvonne,

This is very low mileage for a catalytic converter to fail, but it is likely to be due to the kind of driving the car has been used for. Has it been driven mainly in an urban setting for short journeys? If so that could cause it to fail quicker.

The cost of the part sounds about right, but the labour sounds very expensive. It may be worth asking the MINI dealer to confirm how many hours that is for so you can see their rate. Also, as the car is out of warranty anyway, it's worth popping into an exhaust specialist to find out how much they'd charge to do the work.

Hope all that helps.