J.K.
I had five kids and never gave the binky to any of them (partly because none of them would take it...LOL.) Anyway, without having experience, I'd probably just say (I have a 13 month old too and they understand more than you think they do) "No more binkies!!! YAY!!! Say bye-bye!!!" Then have her throw it away and clap and say "Good job!!" and then don't ever mention it again. She'll forget about it. My opinion is that binkies are good for babies to help console them. At 13 months, I'd think that they don't need them anymore. Take my opinion with a grain of salt though since I didn't use them and neither did my mom who also had 5 kids... Good luck!!