Your question actually brough back memories. Get this; when I wa about 13 or 14, there weren't even exercise videos yet, but Jane Fonda had just put out her Workout Book and a record album to accompany the book. What a scream, right? But my mom used to do it and I was intrigued, it sounded like fun and the music was cool. So I started to join her in the Beginner's workout. We had so much fun and eventually, she stopped and I kept going. When the first Fonda video came out, I did those and here I am, 17 years later, still going strong. I didn't really do any weight training until I was about 16 or so, when our gym class rotation took us into the weight room. By that point, it seemed safe and we had good supervision and instruction in how to use the equipment and how to train properly, etc. Not bad for a public high school in Chicago!
Anyway, my point being that I started out that young and I think it was fantastic. It made me see working out as a good thing and something fun from a young age and taught me about my body and how things worked a little bit too. I think as long as you are careful about the weight training aspect (have her work with lighter weights and make sure she knows about form, etc) and as long as you and your daughter know for her to be aware of her perceived exertion and/or heartrate, I can't see how it could be anything but a good thing. I know it was for me. If it weren't for Jane and my mom, who knows if I'd be in such good shape today. The rest of my family is obese, suffers from everything from diabetes to high blood pressure and none of them are active. So why not let her take advantage of growing up in the age of fitness. Personally, I got in on that just under the wire! And speaking from my own experience, it can be a really fun bonding activity for you and your kid. And come next field hockey season, I'll bet she'll really be able to kick butt out there!
And not to slight Cathe (because I do ADORE her workouts) but another terrific instructor who actually has tapes geared towards kids is Mindy Mylrea. I think she has one or two vids for that very thing, just if you're looking for more options.
Hope that helped even a little bit. If not, I had a nice trip down memory lane!
Take care