My 3 year old daughter keeps having random nose bleeds. She seems petfectly well no fever runny nose or anything. What could be causing this?

Nose bleeds. In children of this age the most common causes are (1) dry air, which could be improved with a humidifier; and/or (2) picking at the nose, which most children this age do. Another thing you can do to reduce the effect of dryness and itching (which leads to the picking) is to put a thin layer of vaseline inside the nose to keep the membranes moist.