S.S.
I'm hearing two contradictory messages in your post. On the one hand, you seem frustrated with the daycare for what seems like criticism of your daughter. And you're right in as sense: as a rule, daycare providers do not have the education they would need to diagnose AD(H)D. But they are saying to you that compared to the other kids, she seems less able to control herself.
On the other hand, you seem to have noticed the same behavior in your daughter yourself and have concerns. So decide how you feel you can address them. Can you work with the daycare differently? Can she get more exercise? Is she getting enough sleep? You might want to try simple diet changes or add omega 3s, which some folks swear by.
As a mom of a ADD kid, I can tell you AD(H)D is real and it is frustrating, but it is also overdiagnosed and overmedicated. Ask around and be sure if you take her in for testing, it is someone you can trust. And keep in mind that she is awfully young for a diagnosis, which the daycare should know.
Our kids come to us as they are and we do our best. They have challenges and do things we wish they wouldn't, but that doesn't make us failures as parents. Don't be so hard on yourself, you will find a way to make this work.