Any of these should be suitable: Digikey 1.3A Trip PTC List
A good choice that's cheap is the MF-RX065/72-0-ND, it should do nicely.
Here's it's trip curves. For a direct short, it should trip in less than .1 seconds with 10 amps of current. With a partial short of 4 amps, it will trip in under 2 seconds. With #22 wire, that is plenty fast.