Is there a fucntion to share a JotForm quiz on a user's FB timeline as a post

You will only need to share your form's link, this guide will help you to get it: https://www.jotform.com/help/401-Where-to-Find-My-Form-URL 

And the following link will help you posting links on Facebook: http://www.wikihow.com/Post-Links-on-Facebook 

I hope this helps.