I would strongly advise against doing a PGCE straight out of university.
I would encourage your child to go and get a different job for at least a couple of years first. Teaching is so all consuming for the first few years - they would have very little social life while training, and going from education straight back into education is very limiting on their range of life experience.
I knew I wanted to be a teacher while at university, but I waited 5 years before training. In those 5 years I became a senior manager in a different career, worked abroad for a year, and had loads of fun living it up in London with my friends. By the time I trained at 26 (still incredibly young in retrospect!), I had some life experience under my belt, had seen the world, and had plenty of professional competencies. I had also matured, and put distance between myself and my own school days, so that I could come back into a school environment with fresh eyes. I was also no longer practically a contemporary of the oldest children I would need to teach.
I've been teaching for well over a decade now, and the teachers who come straight into the classroom from the classroom are always the ones who struggle the most, in my experience. They're too young and not mature enough to cope with the emotional as well as the professional side of the job. Too many 22 year old teachers try to manage classrooms by becoming mates with the kids, and it always ends in tears.
To actually answer the question, both university and school-based PGCEs have their positives and minuses and it's really up to what kind of person you are and how you prefer to learn. I did a school-based PGCE and I loved it because I was teaching from day one, which was what I wanted. I also really valued being a member of staff in the school and feeling part of things for the whole year (and I ended up staying for another two) rather than being just a student teacher. Others prefer the gentler introduction of the university-based PGCE. I also got paid a salary to train, which was a big motivation for me to do the schools-based programme, but if I'd been able to get a bigger bursary on the university course, I might have chosen that instead.
There are not enough Geography teachers and too many History teachers, so if your daughter wants to teach Geography, a Geography PGCE isn't a bad idea in terms of future employability. In many schools, History teachers have to teach Geography and vice versa anyway, so she'll probably be teaching both throughout her career. The PGCE is more general skills than subject based - it doesn't teach you how to teach your subject specifically - it's your time in school that gives you that knowledge. So on her placements she could make it known that she has a History degree and ask for opportunities to teach both so that she ends up with equal confidence in both subjects.
Good luck to her!