My daughter is set for a science career AND a GCSE in Drama
Yep, mine too. @HypnoRuler is spouting bullshit. A well educated person has a balance of different subjects. And fwiw, my dd has learned a great many more useful skills from her GCSE drama than she did from GCSE statistics. I will concede that history was also useful.
OP, I think it's a question of how well your dd will cope with the performance aspects of the subject. The performances are actually only worth a relatively small proportion of the marks, but she will need to spend a lot of time working on these, including time for rehearsals after school etc. She will need to be ready to work in a group with the other kids and do her fair share of the work. That doesn't mean that she needs to be super-confident, but she will need to be willing to get stuck in and have a go. She also needs to be prepared for the fact that the kids are often asked to critique each other's performances.
My dd loves her drama group and they are generally incredibly supportive of each other. They don't judge people for being shy or less confident, but they do get fed up with the ones who don't contribute and put in the work, and typically nobody wants to go in a group with those kids.
If dd really enjoys it and is willing to put the work in, then I think she should go for it, but the workload is heavy in comparison to other subjects, so she needs to bear that in mind! If she decides against it, how about signing up to an extracurricular drama group instead?