Hi there. Well, first grade can often be a huge transition for a lot of kids. Often it is the first all day experience for a child and even if it isn't, it is the first all day experience with expectations for behavior and work to be done. So don't feel alone.
What are they doing in school besides isolating her? That is difficult because what often happens, kids that are seen as the kids that are causing trouble/getting in trouble begin to become outcasted a bit. Rule followers have big issues with these kids and they start to steer clear. By no means do I think that is fair so I wish teachers would find ways to deal with it that didn't draw singular attention to a child especially since it is often transitional in nature and kids mature out of it.
Your daughter can indeed just be immature. At six, she is at the age in which she will begin to be able to use good impulse control. You should start to see improvement with that. I would encourage her teachers to use a reward approach with her to help her along. Also, I'd want the school counselor involved to help with instructing the class.
Now, my son has sensory integration disorder. But he had signs of it all along. And add/adhd can only be diagnosed if it shows itself in more than one place (so her behavior at home factors in). However, there are things that we do with our sensory son that would help any kid in school. Examples are physical activity. I swear on this---- it has a calming effect on kids. After school, your daughter needs some sports/physical activity. During school, she should have some opportunities to get some movement to help her stay calm and to keep her focused.
We used to do things at home to help with school. For example, my kids couldn't talk to me unless they raised their hand for a period of time each day. I ignored them completely unless they raised their hand and I called on them. Sounds dumb but it helps with that impulse control. We also read some 'social stories' that I got on ebay. Written for autistic kids but don't let that scare you. They were very helpful. They talked about how being quiet in school is being a good friend to other kids. Why? Because the other kids want to listen to the teacher. A good friend lets them listen. Things like that.
Also, teach your daughter to give herself a tight squeeze when she is having a difficult itme in school. (give herself a hug is what you can call it). This provides calming pressure that helps some kids settle.
and ... a lot of children have been misdiagnosed when they do not have it and put on strong meds with awful side effects..Teachers should not be suggesting that a child has any disorder .
If she does have it, that's ok. There are a lot of options for her. Therapies, medicines, homeopathic treatments, etc.
A lot of people have it, it's very common. My husband has it, he was diagnosed as a kid of about 6 or 7. His parents never got him into therapy or medications, totally against it. He is fine now, relatively speaking. Google "untreated ADHD or ADD" and you'll see the effects of leaving it untreated. It's very, very important to have her diagnosed. At least then you'll know and you will be able to make the best choices for her and her future. Good luck.