This so sudden thrusting-on of fame paralyzed every fiber of her being, so much so that she could not keep herself in countenance for very long in public.
Is this an idiom?
It refers to the transitive use of “thrust” in conjunction with “on” or “upon”. This is a more unusual way to write that particular turn of phrase.
It might go back to a well-known line from Shakespeare:
That is a variation of an idiom, namely "to have (x) thrust upon you"; which means to suddenly, unexpectedly, and unavoidably receive something that you really didn't want. (Note that the past tense of "thrust" is also "thrust", and the past tense is what's being used here.) It's the same grammatical construct as "I had water sprayed upon my face"; a passive past-tense, indicating that something was done to the subject (as opposed to the subject performing the action).
Fame is very often the thing being thrust upon people who do not want to be famous; they do something that is deemed noteworthy or heroic and are the sudden subject of a media frenzy, when all they really want is to get back to their normal routine and go on with life.
So, in the quote, someone is having fame thrust upon her. The author chooses to use the action as a noun phrase, and so needs to convert it into a gerund; and so "having fame thrust upon you" turns into "a thrusting-on of fame".