Detox, I really feel for you. Its a horrible situation to be in and lots of us here have been there.
I have to agree with Beca and Atilla.
Not one teacher I know of, including the really good ones, would be able to spot AS in a young girl. Girls present very differently to boys with AS and it can be hard even for the qualified professionals to unravel what's what and give an appropriate dx. There's no way they would dx your dd with anything unless she has it. Dx are hard to come by, often even for children with obvious and clear traits.
Historically, teachers don't even have to complete the SN module of teacher training, as its one of a number of optional modules and even if they do, if wouldn't give them enough knowledge/information to be able to easily identify AS in a 5 year old girl.
I went through similar with my ds. I was fobbed off from Reception year right through to year 3/juniors, when he had a breakdown from trying to cope and hold it together at school every day.
He is now 9 and received his dx of AS in January 2011. Since then things have improved no end for him and he's gone from an anxious, stressed, unhappy, school-refusing boy to one who is happy and thriving at school. I really wish I had gone to the GP sooner.
The route we took to dx was GP - referred to Community Paed - referred to local ASD Assessment Unit. We also brought in the emergency Ed Psych team into school and they contributed to the assessment process, but this was because his emotional state was so fragile at that time.
My ds loved school right up until the end of year 2, despite being constantly bullied for 'being different'. However when he went into year 3, he couldn't cope with all the additional responsiblities and changing social aspects of school life and it was heartbreaking to see the result. If I could have my time over, I'd have him down to the GP in Reception year in a heartbeat in order to protect him from what he's been through in the last few years.
My dh was also of the opinion that I was over-anxious and probably wrong to start with and his family are completely unaware of ds's. He did however, realise how wrong he was by the time ds2 was at the end of year 2 and has been supportive, in a kind of hands-off-ish way ever since.
My best advice would be go to the GP with a list of your concerns and ask/tell them to refer you to a paed. In the meantime, perhaps book an appointment wiht the school SENCO to discuss your concerns, as she/he would be better placed to have some idea, although still not qualified to dx.
If your dd does go through an assessment, you don't have to tell anyone that you don't want to know and that includes your Mum and any other naysayers. You have to do what you feel in your own heart is right and fundamentally, its no-one else's business.