@dlowan,
My early experience would've been so much better if an adult told me that those feelings are not bad, that there are more people like me with lots of different stories and that transitioning is an valid and viable option. I'm not saying that all the children that show gender dysphoria would like to or benefit from transitioning but I think it would've helped me deal with this a lot sooner.
I took a long time to recognize my trans idenetity for many years because of the negative representation of trans people I saw in the media: Ace Ventura, Jerry Springer. When there was a serious discussion it was always "I knew since I was 3", "I never liked any sports or videogames", "no one was surprised when I came out" and I couldn't identify with any of it. I was confused for so long it was only until I saw an trans internet forum where I read so many happy people that had a similar story to mine that I started to realize it really was an option for me.
Times have changed and there a lot more positive examples of trans people in the media. Jazz Jennings is the first name that comes to mind that could speak to a pretty young trans audience, she has a show called "I am Jazz".