Mono is a viral infection, not a sexually transmitted disease. For 95% of people, it is easily treated with

-rest
-taking NSAIDs (like acetaminophen or ibuprofen) to reduce fever, headaches and sore throat pain
-drinking plenty of fluids
-refraining from any strenuous physical activity
-taking lozenges or gargling for sore throat symptoms...
To my knowledge, even if she does have complications from mono that require more serious treatment, it will not cause sterility or fertility problems for your daughter.