I'm a teenager myself, and I know friends of my age that have got the implant whilst being a in a relationship, only for that relationship to break up. The implant should really be for people that are in really long term relationships because it's in there for 3 years, putting hormones into your body and if it's not used it's pretty pointless. And really it shouldn't be needing use at 13 years old, that's 3 years underage and I think it's great that she is willing to talk to you and ask you about sex but she should be discouraged from becoming sexually active, mistakes can happen and imagine if she were to fall pregnant at that age, it would be devastating. Honestly, she is more likely to wait until 16 if you talk to her about it, that's what happened with me. Also, most Dr's wouldn't be happy to give an implant to a 13 year old, even my friends who were 16/17 needed to persuade them.
Good luck!