My dad always said buying a used car is just buying someone else’s headache. Maybe your current used car is giving you a little headache right now, but what makes you thing another used car will not? If you have taken care of this car, and you love it, and it is otherwise in good shape, then spending $1500 on this car is nothing.
But first you should back up a little bit. I have a car with over 300,000 miles on the same catalytic converter. Converters generally don’t go bad unless there is some other issue. So first, what exactly has a shop telling you that you need a new one? Be as specific as possible. If there are computer error codes involved (which I’m sure there are), then report those (format: “P1234”). What kind of shop is this? And second, if they can determine for a fact that you need a new one, have they tried to figure out why? There is usually a reason.