Do not plead guilty. Maintain your version of your story.
If she says, you are speeding and hit her headfront, according to
physical theory, there should be a dent or markings in front of
your car even if you are travelling at 50km/h and hit an object.
Some more the object now is human, its so big.
Keep on emphasing that she hit your left rear. Die die also say she
hit your car left rear. You need to sound firm and very very
confident when going for the interview with the police. Sometimes
try reasoning.
Like e.g " if i am speeding and hit her head front, she would have
fly forward and not at my rear." Normal road is 50 - 60km/h, if I
am speeding, it shows i will be travelling at more than 70km/h. If
I am travelling at more than that speed, she should be laying in
the hospital now and not standing like nothing happen and saying so
much nonsense. "
Push all blames to her and request for a review in the
investigation process.
Even if she is hit by your car, the proper procedure is that she
would need to go for medical checkup and come out with the physical
injury report done by the doctor. If the report says nothing wrong,
use that as additional evidence that she is telling lies.
According to what you say on the scenerio, it does not justify to
24 demerit points and $3000 fine. Even if you are guilty, on the
average for such cases on first time offender is normaly 6 - 12
points or fine $1000 or both.
My fren was in a similar situation like yours before, but he won
the case with some "inside" help. The police grill the pedestrain
for the truth untill he cannot take it and drop the case.