Take it easy until you've learned how fast/hard you can corner without pedal strike. Just about everybody dumps it a couple times when they're first starting out. Take it easy on unfamiliar corners as well. Road conditions and camber can make pedal strike more likely.

Is this a road frame conversion to fixed gear? If so, how long are the crank arms? Road frames tend to have lower bottom brackets (and thus less ground clearance) than true track frames. Shorter crank arms will lessen the likelihood of pedal strike.