You say you dont have a case because there is no paper trail, then start making one.
Email her, you ordered xxx cake, for xxx date for an agreed preice of xxx amount to be paid in 3 installments, then list the first installment and the date it was paid.
Then list balance due.
BLIND CC Yourself on the email.
When she repsonds with her excuse, you have begun your paper trail.
If she does not respond, send the same again, add a note that a late fee will be added for...