Under the post was a screen shot of the victim's Facebook profile, with her name and a photo of her with her two children.
Comments on the post suggested the victim "had better start digging her hole now".
The next day Weston named the victim again in Facebook posts and a video.
In New Zealand, victims of sex crimes have automatic name suppression.
At sentencing, the court heard Weston had completed two years of a three-year early childhood teaching course, and was seeking a discharge without conviction as it may prevent her from furthering her career.
Crown prosecutor Justin Marinovich said the level of offending was serious, and the court was told the Crown opposed the application.
Judge Timothy Black said the entire experience had a profound impact on the victim.
"The victim was raped by your father, and has had to relocate to Australia to avoid threats made against her" he said.
Judge Timothy Black accepted Weston's behavior was out of character, but that it was appropriate to categorise the offending as serious.
The court was told a conviction would not prevent Weston from registering as a teacher.
Last week Dennis Weston was sentenced to nine and a half years for rape.