I have one dancer (currently competitive, was at a serious ballet studio from age 3) and one Optional competitive gymnast. I have been around the dance world for a very long time, and I coach competitive gymnastics.
Over the years, I have seen several girls who went between dance and gymnastics, some focusing more on one or the other, some trying to do both which is truly only possible up to a certain point. At some point, gymnastics training becomes detrimental to ballet, although I don't think the opposite can ever be said (I'm a firm believer that a weekly ballet class would improve almost any gymmies gymnastics..! ).
I have seen some girls with compulsory level gymnastics training make the switch to dance and do fabulously well in the competition dance area, especially in the junior category where tricks are often more rewarded than pure dance technique.
The thing about competitive gymnastics is that it is a very age dependent sport. You want to get the training in at an early age to truly "have a shot at it". Dance can be returned to and is a much slower boil. You can continue to dance in some form all through life, and although I know there are many exceptions, most gymnasts do not continue very long past college age, if that..!
If it was my kid and she was equally passionate about both, I would allow it as long as possible (finances and time allowing, of course). If there really is only time and money to do ONE, I would probably at this point try JO gymnastics but keep an hour dance class/wk or so. She can always go back to dance next year or in a few years if she changes her mind, whereas competitive gymnastics is much harder to get back into and requires more physical preparation to be safe. (Yes, of course I'm well aware that dance is incredibly physical as well, but slightly easier to maintain with less hours)
Ultimately, it would have to be my DDs choice though. It is, as much as us parents get involved and emotionally invested, THEIR journey. It doesn't really matter how much *I* see my child as a dancer/gymnast/soccer player/artist or how much talent they would be "wasting" by choosing something different if it is not THEIR passion. At the higher levels of pretty much any activity, you need to be passionate about it to want to do it. My girls spend way more time at the studio/gym than they do at home!! There is no way I would let them continue their activities if they weren't 100% into it, regardless of how much talent or whatever they have for it or how much I would love for them to be a dancer/gymnast/soccer player/artist. It has to come from them.
Also, kids change their minds about things. A lot. What they are passionate about at age 8, may be completely over by the time they're 10. Don't let YOUR ideas of a long time passion for your DD interfere with this. 2-3years from now she may no longer be interested in any of these two things but instead want to play volleyball..!
As a side note, it has been mentioned already, but accidents and injuries can happen in any sport. A friends DD just had knee surgery at age 15 from playing soccer. My 15yo dancer has had multiple injuries including hip problems that has required lengthy physical therapy. One of her dancer friends broke her neck (yes, you read that right) doing a simple floor move. She has recovered but was in a neckbrace for about a year... My gymmie has dealth with her fair share of injuries, but nothing earth shattering. Any physical activity has its own risks for injuries as well as for overuse problems. My DH cannot watch gym practice anymore because it terrifies him to watch DD attempt bails and doubleback dismounts on bars as well as flipping vaults. Just too scary for him! I see it all day long and know how qualified the coaches are and how much drilling and shaping goes into everything beforehand, plus how mats/pits are utilized etc all in order to make it as safe as possible. Accidents will happen, but if it's any consolation I have known very few serious injuries to actually happen at gym. Most of our hurt gymmies have been injured outside of gym or doing completely sily things like stepping off a mat or something..!
Best of luck in whatever you two decide. She is so young, you have some time to figure it all out!
On the other hand, she is more athletic than graceful and definitely built more for gymnastics. We are not at a pre-pro or competitive dance school so the hours are not likely to increase much more that what she is already doing, and maybe I am overanalyzing things. She is not even on team and she really is enjoying herself. I also really like the girls she is with - very welcoming and warm to a newcomer, and the coaches - tough but warm. Any thoughts would be welcome 
