I don't know your school and can't possibly predict what they would do. But I would wonder which is more likely to result in them wanting your daughter to leave: problem behaviour, or a diagnosis that can reduce problem behaviour. If you know why your daughter is experiencing challenges, it's much easier to support, remediate, accommodate, whatever is needed. If necessary, the heavy lifting can be done at home, so you do much of the work, but the school can reap the benefit.
If - and obviously it's a big "if" in a six-year-old - she has a learning and/ or attention challenge, there is lots that can be done (most of which is not medication) to help build and/ or compensate for missing skills and processing deficits. The earlier the better. The longer these issues are left to grow, the harder it is to help.
