At £1200/month you should be able to find a nice place to rent. You say you want a min 2 bed with garden - would a "conversion" be OK for you? That's when larger houses have been subdivided and you still have your own garden or bit of garden? Lots of places in Pollokshields like that: lovely Victorian stone built houses that have been split in half (like our home) or for the larger villas, split into 3 or more "flats".
Dh calls our house a "horizonatal semi" and we have an enormous back garden (spit left and right with our downstairs neighbours - some are split front and back) and we share the front garden.
Local secondary is Shawlands Academy and is excellent. Ds finished there last year and is now doing well at Aberdeen Uni. Turns out well-rounded young people, ready for the individual learning required at Uni.
Excellent public transport: buses, 2 or 3 different railways lines and (if you're at the right end of Pollokshields), even a dinky wee circular subway
. Lots of parks to enjoy - and by next year (I think) the Burrell Museum should be open again following its reburbishment.
The exams are different up here, but if she can come up straight after her GCSEs, ready to go into S5, which is the equivalent of Y12 (when Scottish pupils sit their Highers), then she should be able to catch up with the different curriculum. It is usual for Scottish (academically capable) kids to sit 5 Highers and then, if they choose to stay on for S6 (technically, they can go to Scottish Unis after S5, although nowadays most stay on to S6), can do 1-3 Advanced Highers and/or a crash Higher (done in a single year, not having done the equivalent National 5 itself roughly the equivalent of a GCSE ) or re-sit some Highers or Nat 5s). For example, ds took 2 Advanced Highers, in Maths and Physics and a crash Higher in Modern Studies. (Advanced Highers are the equivalent of A Levels).
The reason I suggest coming up straight after the GCSEs is that Scottish schools often start the following year's timetable in the June before the summer holidays, after the exams have finished. You should also be aware that Scottish schools tend to finish at the end of June and start back in the middle of August. (Private schools are slightly different - tend to start back in September).