Pilot reported beginning to snake due to rudder over-correction and pilot-induced oscillation on takeoff.

Narrative

Event occurred after touch-down and touch-and-go. During acceleration to takeoff; pilot began to snake [yawing motion about vertical axis] due to rudder over-correction and pilot-induced oscillation (PIO). Pilot determined that continued acceleration and rudder correction would result in roll-over and so cut power and applied brakes heavily. Aircraft was headed towards south-east corner of intersection between BFL Runway 30L and Taxiway E. Pilot adjusted direction to right to avoid nose wheel collision with runway light; resulting in glancing hit to left main gear. This resulted in damage to the runway light and wheel pant fairing. No additional damage to tire or landing gear could be identified by pilot. Likely caused by rapid application of power without appropriate right rudder correction. Over-correction by pilot led to lateral PIO. A cross-wing gust may also have contributed but unable to determine. Gusting conditions were reported up to 15 kts. at 20 degrees from runway heading. More gradual application of power and/or earlier identification of PIO could have avoided incident.