I went to an all girls boarding school at 11 and my brother to an all boys at 13. We both started school in the bottom year and in my case the school expanded rapidly at 13 as all the CE students joined then.
We both loved it. We lived in India and had a bad home life so boarding school, for us was the perfect place and I begged to go. My mother came back to the UK a year later and my relationship with my mother was only strengthened by her getting to play good cop all the time whilst school was the mean old bad cop when need be.
My school, Benenden, used houses purely for sleeping and pastoral care with a school central eating area and central classes. My brother's school, Tonbridge, was much more house based with all meals taken in house and lots of subjects, especially sports, in houses too. My brothers system was great if you got on well with those in your house and my brothers school friends are all from his boarding house. Mine gave me a wider range of friends and meant I wasn't "stuck" with those in my house. My closest friends from school weren't in my boarding house.
My school was all boarding and we had a wide mix of girls from overseas, down the road and across the country. I do think that a total boarding school is much better than a day/boarding school as boarding only schools tend to put a lot more focus on weekend activities which is important.
Certainly at my school we really did develop tough hides, independence and were quite grown up. The opportunities I got from my school I would never have received had I stayed in India nor would I have had them if we lived in the UK: Choir trips in Europe, sport trips to America, constant cultural trips (Christmas markets on the continent, theater in London etc), lectures such a wide range of people as Julian Fellows, Bear Grills (before he became famous), an old girl who had been part of the 9/11 relief effort, radio presenters etc. We performed school plays at Her Majesty's Theater and others. Even now I'm happy meeting new people and can chitchat like a champ because we (even at 11) were expected to be total ambassadors for the school. Parents were taken round by students and visitors had dinner with girls and the odd staff member.
Your days don't really stop which is a good thing when you're far from home. I remember having a full days school (8:30 - 5) followed by team sports practice, choir, dinner, prep, school play rehearsals and finally going to bed at 10 happy but tired.
Going to a school in the middle of no where is an advantage when you're younger as it is safer and when you are older there is no local pub to pop to. When you're 18 and want to go out it's a bore though!
There really is a high level of care given to students within the houses. We were close to house staff and had personal tutors who looked after us and cared for us. There was always someone to talk to and you never ever felt alone. The schools know too that it's tough for girls who are miles away from their parents. You aren't given time in the first month to get home sick and staff keep a close eye on you.
I also think that expat children grow up quickly anyway. Certainly at my school girls who lived overseas were far more grown up than girls who lived in the UK.
An all girls school is as bitchy as the girls in it. In my experience it depended who your friends were. Some girls, of course, were competitive and jealous and bitchy. Most were rather down to earth and didn't care what car your parents drove or where you went on holiday. This is exactly true at ANY school. The benefit of girls only I still feel strongly. No one worried about doing their hair or make up in the morning and girls who did fuss about make up during school time were thought to be a bit sad.
I would send my daughter at 13 if I felt she wasn't ready at 11 and yes I would send my daughter if I felt it was right for her. No school is right for every child and that is certainly true for boarding schools. You also need to visit schools carefully and make sure you send your daughter to one that fits her. Some are more sporty, some more academic and some more arts based. It depends what your daughter is good at.
Good luck.