She'd be allowed to, but you'd probably pay international fees. If it's a permanent move then personally I'd forget GCSE's, they'll be no use to her in the US anyway and I can't see why you'd put her through the stress of that for nothing, particularly as it will then also make her final two years in a US school more stressful as she'll be trying to cram stuff in and get her GPA up in a short amount of time. Better to get her in a local school asap so she can start making friends and getting to grips with the subjects and preparing for college IMO. College prep starts years earlier in the US, she'll need to be doing all sorts of extra curricular stuff if she wants to go to college there, and a US school will be well versed in that.
JMO though, and obviously she's your child, but if we'd been moving permanently and our son had planned to go to a US college, there's no way we'd have put him in a British school.