I have not read any of the other answers, so please forgive me if I am repeating what others have said.
First of all, definitely let the school test her. I knew something was "off" with my son basically from the moment he was born and the doctors completely ignored me. I basically got to the point where I was begging someone to look at him. He finally got evaluated when he was 2 and he had sensory integration disorder. This is NOT autism, but a lot of kids with autism also have sensory integration disorder. When he first got diagnosed, I was scared to death that he was going to be "tagged" and treated differently. But, what I did not realize is that because he now had a diagnosis, he was FINALLY getting the help he needed. Instead of having to go outside with all of the other kids onto the sand that he HATED, he was allowed to NOT go out onto the sand. The school HAD to have a different activity for him. Eventually he was able to go onto sand, but he wasn't thrust onto it with no care. And, with a diagnosis, the teacher's now realized that he was different (officially) and he wasn't just acting out because he couldn't cope. He just flat out couldn't cope and with a diagnosis, it was now THEIR problem. They had to do something different. When my son was diagnosed, he was in a pre-school which turned into an elementary school. He stayed at that school for Kindergarten and 1st grade. During this time period, he was getting occupational therapy, physical therapy, and speech therapy. By the time he was in 1st grade, I would say that you could not even tell he had sensory integration disorder. But, because the school knew about it, he was dealt with if there was an issue (and dealt with with open arms - not as a problem child).
He transferred to a public school in 2nd grade. I did not even reveal any of his issues to the public school because they were all essentially gone. BUT, the public school came to me and said he needed speech therapy still. He's in 3rd grade now and STILL getting speech therapy. So, for me, the access to the public school resources is AWESOME. Further, I found that the public schoool actually has better resources and more acknowledgement of problems and the ability to deal with them. So, I would not discount the public schools out of hand. Do your research, let the schools do their assessments and then make a determination.
Through my experience with my son, the main thing I discovered is that YOU are your child's best advocate. The kind of help your daughter gets is entirely up to you. And, honestly, you may have to force the school to comply with some of the requirements your daughter may have. But, I can promise you that without a diagnosis, the school will not help you. With a diagnosie, the school is obligated to help you. I'm not 100% sure what the rules are with autism, but I THINK she might be entitled to an assistant and she also might be entitled to not have to deal with LARGE group assignments. So, that is why I am saying do your research and definitely let them do the assessments. IF she is autistic, that opens your world up to some resources that you currently do not have access to. And trust me, take advantage of the resources.