Uncharted Territory

First of let me start by saying, I realize that Sarah is only 4 and has only been in school for a little over a month. I also realize that she is very headstrong and has trouble listening at home from time to time. She is very chatty and very easily distracted. I think she could be called a trouble maker at home.
Having said that, she is a beautiful girl who is very smart and can be incredibly focused. She can write very well, she can do a 100 piece puzzle, she can color and stay in the lines, she is becoming quite the artist. She has an incredible imagination, creating games to play with Emma. She is incredibly active and loves to run, jump, dance and gymnastics. Her enthusiasm for things is bottomless, she can get as excited about a receipt as she can about a beautiful new doll. It's quite contagious. It can be pure joy to be around her. I love her with all my heart. All of these words and descriptions are mine and I'm not afraid to say that she can be quite a handful and sometimes I don't know what to do with her.
Her preschool teachers give out awards for good behavior every day. She was so proud of them! But then last week she didn't get one and she was very sad and cried in the car telling me about it. Then it happened again, to much talk during circle time. I just said "Try harder tomorrow and hopefully you will get one. It's up to you, it's in your control."
On Wednesday, not only didn't she get an award, she got a note sent home about her behavior, she was talking during circle, argumentative with her friends and she growled at another teacher on the playground. I tried talking about to her about it but couldn't quite get a straight answer from her about what had happened. I was upset, but figured she was having a bad day. Everyone is allowed to have one, I wasn't happy but thought it was an isolated incident and she would have a better day on Thursday.
On Thursday, I thought about her all day and sent all my good thoughts and wishes to her. I just didn't want her to get another note. When I picked her up she came running out with an award that said "Better day" I was so relieved. Although while Sarah was telling me about her day, I found out that she still had to sit in time out during circle. My heart sank a little. But she seemed so proud. So I let it go.
So this morning when we driving to school, I told her that if she had a good day and didn't have to sit in time out, when she got home she could have a treat. Not sure if this was the right thing to do, but I so desperately wanted her to not get in trouble today. She thought that was a good idea. So I left her feeling positive that she was going to have a good day.
When I picked her up, she came running out of her classroom and she said "Mommy it's a pattern, note, reward and note." (which I thought was very clever, but still my heart sunk). Today her note said "Talking to much during circle and not listening to Miss Lynne." I tried to talk to her about it, but strangely she didn't want to talk anymore.
I'm just not sure what to do about it. Do I do anything? Is she just becoming so comfortable there that she is acting like she does at home? It just hurts my heart that someone else is cross with her or thinks bad thoughts about her. I know this is a lesson that I need to work on for myself. She clearly loves school so these notes and time outs are not affecting her outlook on school. I'm so glad about that. Am I just projecting my own insecurities on to her? Am I worried that her behavior will reflect badly on our parenting? The answer is probably to both these questions. This is another thing that I need to work on for myself. Conversely, since she started at school, she has done so much better at home. She is listening better, her temper tantrums are way down and things are good around here.
So I'm going to continue talking to her about it, but are there consequences for her at home if she behaves badly at school? Or is to early, it is only preschool. I would like to give her positive reinforcements when she has a good day. I feel badly that already at age 4 she doesn't want to talk to me about it. I want her to be able to talk to me about anything, I guess this is yet another thing I really need to work on now so it doesn't get worse as she gets older. I just feel like I'm in uncharted territory, I don't know quite how to proceed. I don't want her to get labeled as a troublemaker and have that affect her great attitude toward school. She will always be my baby girl and I want the world for her. She is becoming her own wonderful self though and I think she will always be on the chatty side, that she did get from me.