Detecting short circuit (max4080)
From the linked datasheet, the output is valid when the common mode of RS+/- is 4.5-76 V. You will be able to measure current accurately until your 15 V / 1 A supply is forced below 4.5 V output by its overcurrent protection. What are you trying to use short circuit detection for? If you want to protect the power supply, you will need additional circuitry. If you want to know the power supply status and its self-protection is adequate for your application, can you get that as a feature of the supply?