Chances are very good that she can avoid a moving conviction if the ticket is in Jefferson County. I am familiar with Jefferson County. If it is in Jefferson City she needs a traffic lawyer in Jefferson City (Cole County). There is no court supervision in Missouri. That is an Illinois procedure.
What she does not want to do is pay by mail. If she does that she'll be convicted of the moving violation in Missouri, and it will also show up as a conviction in Illinois.