DD wants dance career but not sure she’s good enough!

I agree with this.
And by 10 you do know who is good enough

You can work in dance in many ways, so she can follow her passion but perhaps focus on longevity of a career, so look at teaching, production, choreography, anything theatre related. I have a cousin who went through football youth academies for very good teams and although never quiet the best, had a little success as a youth player, however it was not to be so in his early 20s. He loved football so much he took all the coaching, psychology courses etc. alongside recognised international qualifications and ended up managing a very successful club and is still in the profession, in his late 60s as a scout! You can follow your dreams in many ways and often those with the greatest passion make the best teachers. Just broaden the conversation about how to make dance a career.

At this age, focus on the fact that she's doing regular exercise that improves her confidence and core strength. Levels of teenage girls doing regular exercise drop away, so keep it going whilst you can. Maybe help her to look at options around dancing - can she sing as well, would she like to work on a liner etc. rathe than just be a ballerina

Hard work and dedication are what matters most. Unless she really isn't flexible or has no musicality she's as good a chance as any of fulfilling her dreams.

If we were talking about someone wanting to be, say, a medic with average grades, then I’d absolutely agree with you. But dance is different. My DD is a very good dancer. She loves it and works very hard. But she’s never going to be a ballerina - she doesn’t have the right body shape for it. So while I encourage her to pursue it as a lovely, positive and healthy hobby, I’d never encourage her to go down that track as a career.

She's 10 years old dancers train for years why are you writing her off at 10.give her and you a break and let her develop her interest and see where it takes her.

Is the school a good one generally?

I wouldn’t discourage her but I would talk (in an age appropriate way) about the importance of her education generally as well as dance. Most girls who are keen on dance don’t go on to be professional dancers and that’s something you can talk about (without putting it in terms of “I don’t think you’re good enough”). There are also plenty of ways to have a career in dance without being a professional dancer, from set design to arts administration to teaching to physiotherapy and nutrition etc etc.

I thought you were going to say DD was at least 16. That's so young to have any idea of the future. Definitely let her pursue it but also make sure she's aware how important it is she gets as good grades in GSCEs, A-Levels etc so she has that as back up. Even if she does make it, an injury could end all that so easily.

Hard work and dedication are what matters most. Unless she really isn't flexible or has no musicality she's as good a chance as any of fulfilling her dreams. I can think of quite a few girls that did festivals with mine aged 10 who mine would usually place higher than, but this all changed as they got older and for mine it was more a hobby and the others took it more seriously.

Be careful about indulging this, make sure she knows that she needs an education. Point out that dancers, like footballers, don’t always make it and they need something to fall back on.
A woman I know had a DD that wanted to be a doctor, and we all knew about it ! She paid for a private education from year 5, and so had to do the same for her DS. The DD went off to do A levels at college, realised very quickly she couldn’t do it, and dropped out of college.

Can you get her extra tuition to improve on weak points? Would she be willing and able to hustle and travel for auditions? Can she fall back on family between jobs and travel if necessary?

Those would be my questions. It’s not a life-long career but would make for some amazing experiences and memories! I was a dancer myself, but never as good as the best. My own answers to those questions would have been “no”, unfortunately! I still watch backing dancers and think “Ah, in another life that could have been me..”

Don't nuke her dreams at 10!

She might change her mind as pp says, but in life its the people who are committed and persist who have greater success than those who don't have to work so hard - have a little faith!!

Also, don't teach your child that you shouldn't try just because you think / someone thinks you're not good enough- support her.

I don't have any experience! But would say that she's only 10 so her interests may yet change.
It will be disappointing if she doesn't get the breaks, but personally I would keep encouraging her whilst also keeping an eye on developing her resilience to setbacks.
I would imagine puberty will have a significant effect on dancers too and it's also possible that some of the keener girls may drop away over time.
I would just have her back for now.