The law is different everywhere, so I can only say what would happen in Victoria. There wouldn't be any question of reporting the incident to the Nurses' Board if this was the first drug error.
The nurse who made the error would write an incident report, describing what happened and why. The report forms we use include tick-the-box sections asking about factors that contributed to the incident (including inadequate staffing and inadequate education) and factors that minimised adverse outcomes (including quick detection and good luck).
A resident is notified, reviews the patient and documents anything else on the incident report, which is then signed (and expanded up on if needed) by the nurse in charge. It the goes to the oversight committee, who look at contributing factors to critical incidents, in an effort to alter system-wide issues.
The error would be documented in the patient notes, and the patient would be notified and monitored.
Determining appropriate action regarding the nurse depends on a number of factors: her (or his) experience, how serious the error was, adverse outcome, track record of making mistakes, what contributed to the error, and how she (or he) responded (how quickly they picked up that an error had been made, how quickly it was reported etc).
An example: A graduate nurse on my ward recently changed an infusion pump, because the old one had a flat battery and the patient was sleeping in the corridor, away from any power points. She didn't change the rate on the new pump, and the patient received an overdose, resulting in a transfer to coronary care for cardiac monitoring.
The grad reported the incident as soon as she became aware of it. She has been taken off nights so her practice can be more closely supervised, and she's scheduled for a remedial medication administration session.
Hope this helps