Raspberry PI Zero - 5VDC output current?
Looking at the datasheets at https://www.raspberrypi.org/documentation/hardware/raspberrypi/schematics/README.md, the PiZeroW has no fuse. (Compare for example with the Pi 2B, which has a fuse at the USB input)

Now, a Ws2812b draws 60mA when set to full white brightness (255;255;255). This makes 1080mA, which is already more than what your 1A power supply can output. You may be OK if you don't set too many LEDs too bright, but still, your Pi takes up to 250-300mA on its own. Consider to get a stronger power supply.