We have to be very very careful when prosecuting false rape accusation cases, because the alleged false accuser might be lying when they retract. The police are rather prone to pressuring rape victims, particularly young ones, into retracting allegations. These coerced retractions have sometimes then been used as "evidence" that the victim lied. It's wrong to expect anyone to flawlessly navigate such abuse of police power, and cases like this should only go to court if the prosecution service have made sure that the police didn't coerce the retraction.
There has also been at least one case where a school-aged girl falsely accused a teacher because she was being sexually-abused outside school and knew no other way to get help. Jon Brown of the NSPCC said "where a false accusation is made, it can often be a cry for help from a troubled young person who is in need of help but can't bring themselves to say what has actually happened or is still going on", indicating that cases like the one above, where the victim is truthful about being abused but has misidentified her attacker, are commonplace. Sexual abuse is a situation that no human should ever have to face and it is ridiculously unjust to expect a child or young person to flawlessly navigate sexual abuse and its consequences, including reporting.
I concur with a PP that we shouldn't jail people for non-violent crimes, unless they are repeat offenders or have committed a crime over a long period undetected (e.g. skimming a pension fund for years). Appropriate alternatives to a custodial sentence for a false accuser could include a written published retraction and apology, and monetary compensation to the victim. Garnish her wages if she can't pay the compensation upfront.
Please don't call young women "girls": until I read the article, I thought you were talking about children.