Have you spoken to other members of your department?
In my experience, the subject of assigning grades is not openly discussed. Partly, I think, this is in consideration of the autonomy an instructor has when running their class. However, you should find out if there are any departmental guidelines.
That said, I must caution you not to treat any student differently than any other. for example, giving her a make-up assignment without making that option available to *every* student is a recipe for disaster.
When a student appears just prior to the final exam- a student that has not made use of office hours etc. during the course- I try to encourage them not to panic, to do their best, and leave it at that. Students will cry, beg, plead, and insist that their life will end if they do not get an 'A'. Ignore it, and make sure your office door is always open.