If you've never had a driving offense, your first point of call is to write a letter to the officer that ticketed you explaining your good driving behaviour, ask them for leniency and that it be recorded officially as a warning.

The next step is to take it to court and show cause as to why you believe the penalty was to harsh, I'd argue on the grounds that you're a P plater and never have lost a point and that a 3 point offense puts you on grounds where if you get another traffic related offense you could lose your license. I'd then state how this could lead to undue hardship due to the fact that you wouldn't be able to get to work. I'd use this particularly if you live in a state where there isn't a good driving behavior bond.

Either way any decent magistrate is going to chuck it out, at worst they'll make you pay the fine but not record the points.

Just represent yourself, traffic offenses are really easy to defend, if you have any problems get a free legal consulation and/or ring legal aid, they'll pretty much say exactly what I did particularly if it's your first offense.