The first one that comes to mind is Bindi Irwin, Steve Irwin's daughter. She is absolutely excruciating!

I'm not quite sure how old she is, but she might fit the bill. I've never seen her show, thank goodness, but she's not exactly an actor. I think she does a lot of singing on her show about being healthy and about animals, but I'm not sure. She's always wearing the same khaki clothes as her dad did. The only thing is that she's a fairly recent phenomenon, the last 3-4 years.

I'll have a bit more of a think, and get back to you!