I have a fair amount of experience of CLC. As pp has said, there are many Asian girls there and in some houses the % is as high as 80%. Your DD will feel at home in that sense.
There are day girls at CLC but all those who board mostly stay in every weekend so your DD will be surrounded by lots of friends. They also have plenty of activities and trips out to keep the girls occupied, it's very well organised in that sense. There will also be free time when she can chill out or chose to do things, such as afternoon crafts with staff members. In the week the school timetable is carefully structured.
Most overseas girls go home at major holidays (Christmas, Easter, summer) although some stay with host families. There are also half terms and "exeat" weekends - some girls stay with relatives or host families, sometimes parents come over to the UK and they have a weekend in a local hotel to have time together. The whole town is geared up to this, as there are several local schools in the area so sorting this out is easy.
As your DD is not currently UK based, you will be expected to provide a guardian. It can be a relative or UK friend family, or it can be via an official guardian company which you pay for. They arrange for stays with host families, they check on girls and give updates, and they liaise with CLC's transport department for arranging travel to and from school. Younger girls can travel alone, they are collected from their boarding house by coach or private car arranged by CLC and taken to the airport or whatever, they are accompanied all the way and can fly as an "unaccompanied minor" if you wish. To do this you would make it known when booking flights, there will be some extra paperwork to fill in which the school will print off for your daughter to carry with her. She will be accompanied to the airport and placed on the 'plane, at which point the air hostess will take over and make sure she's handed over correctly the other end. It all works fine.
A very good guardian company which deals with many of the CLC girls is Pippa's Guardians (no, I don't work for them or anything) but there are others in the area, they will help you with everything (eg. Quest Guardians, Oxford Guardians). If you are using a relative as a guardian (such as grandparents) make sure they are aware there may be occasions when they are called upon if your DD is ill. Most illness is dealt with int he boarding house or in the medical centre, but sometimes guardians are called upon too.
One other thing to remember is to not send your DD with too much "stuff". Families tend to send far too many clothes, books, cuddly toys and everything under the sun, it's unnecessary. Just uniform, lots of underwear, toiletries, a few non-school clothes, a decent coat, an umbrella and some wet weather shoes as well as school shoes as a basis. Few few bits and pieces to decorate their dorm area, some photos, just keep it all simple. Some girls arrive with several LARGE suitcases of stuff and it just becomes a bind, they never use everything. However, do make sure EVERYTHING is named, and provide plenty of towels...like socks, towels seem to disappear very easily, no idea why!
I hope that's helpful.