What is the appropriate age for a kid to start light weight lifting?

I don't think she should, not until she at least thirteen. Unless you have small, one pound hand weights and you put in a video that's meant for parents and kids and you do it with her. If that makes sense. I've seen videos that are for parents and their children to workout to. And most of that is baby fat. And you should also take a look at her diet, is she eating healthy calories and fruits and vegetables? Letting a child like, weight train is insane. And I don't mean weight train like this freaky five year old all over the news, even a little is too much, unless you're being fun about it. Like I suggested, the video would be a good idea, or maybe just dancing around for a few minutes a couple times a day (it burns more calories than you'd think).

I started a 12

It's been proved that children as young as five can weight train safely, but I would recommend around age 12.

yes. perfect age is 16, let your daughter grow out her baby fat first, then you can worry about all that other stuff later