Expats come and go at all times of the year, so most schools will accept enrolments as being an ongoing affair. Actually getting a place can be a different story.
I think you will find that the International Schools
here are pretty strict on discipline - but in a different vein to the local schools. I don't know how much detail you will need to give on enrolment (surely the report from her present school would suffice), so if you think your step-daughter can keep her nose clean, I wouldn't voluntarily give the info to the school on enrolment.
As for strengths and weaknesses, that will depend entirely on what you want for her schooling and what she might need. big vs. small; international curriculum vs. country-based curriculum; academic focus vs. sporting/arts/holistic focus... All of these factors come down to opinion really, so you might want to call a few and see where you could potentially enrol her, then visit the schools and see what appeals.