The soil in the pot looks too wet - I'm not sure you have it in a pot which has drainage holes, it doesn't look likely from the image. Whilst Pilea peperomioides shouldn't be allowed to completely dry out, it does not like to be constantly wet, so the top of the soil should feel just about dry to the touch before watering. The fungus is present because the soil is too wet. Once the soil is drier, it will disappear.
If you don't have your plant in a pot with drainage holes, then repot into one which does. When you water, water thoroughly, and empty out any excess from an outer pot or tray after 30 minutes.