Have you noticed what time of day the non-compliant behaviors are occuring? Is it at the time that she starts to give out, at the end of the day,or anytime? This could play a role in her behavior and could be handled with maybe a schedule change! Is she an independant child? The teacher maybe able to provide her with a special task which could be a diversion. Does she have any allergies,frequent sinus or ear inferctions? This may be disrupting her sleep and affecting her behavior. Good luck and she's lucky to have you for a mom!
Due to the fact that we live in a rural area and my children ride the school bus to and from school, we get up around 4:45 in the morning to get ready for school. My daughter has become use to waking early and going to bed early. However, she does have her days when she is up at 2:00 am. And that has been a problem with her being up alone at that time. I find myself waking just to get up to send her back to bed. Lately, she has been getting plenty of sleep and she gets a healthy breakfast *no junk foods* to help her start her day off well. But she gets to about 10:00 and she sort of runs out of energy until lunch. Then that's when she is very very active. So there is a schedule that she normally follows. But to answer your question... She does have her days when she doesn't get a full nights rest but I believe it is because it is so normal for us to be up so early. But even with a full nights rest she is still very active. The only time that she is not is when she is not feeling well. And with that come the easily irritated, very cranky and down right not happy at all little girl. But I've figured out a way to counter those days..
I'm glad your daughter is doing so well. I just want to ask if she has been assessed for sleep problems. I'm thinking specifically of obstuctive sleep apnea or sleep disordered breathing. In children this can be central, or caused by enlarged tonsils, allergies, among other causes. More importantly, children get less quality sleep and can develop ADD behviours to cope. In children with sleep problems that affect behaviour, %80 of the time it's Apnea/Breathing; I also believe I read that children with Down's have a higher incidence of obstruction. I think it would be worth looking at, if possible (many cities have pediatric sleep apnea programs, and it's non-invasive testing). If it were the cause, then you can treat the problem and long term stimulant use can be avoided.
Medication (usually some form of psychostimulant such as Ritalin, Adderall, Metadate, Concerta) can be quite effective in diminishing hyperactivity and thereby increasing attention. Oppositional behavior is usually best managed by way of behavior management, though some oppositional children who also display ADHD sometimes take a medicine such as Clonidine or Tenex in addition to their stimulant medication. It sounds like the evaluation you are undertaking is the sensible thing.