Then I would challenge the school as to why they have requested this.
It is usual to cover your head in a mosque, but I would have thought that mosques that are willing to have school trips to visit would not expect the girls to cover their heads.
It is a sad fact of British muslim life that it's actually fashionable to cover your little girl's head, sometimes in a scarf co-ordinated with her outfit.
I guess muslims are not immune from the image obsessed, shallow, consumerist slant that non-muslims are also guilty of.
I have muslim inlaws and have visited their mosque many times, for parties, events and evening classes.
I am not muslim and I don't join them for prayer (it is a large mosque with function rooms etc). I have not once been asked to cover my head.
However I have 3 daughters who do go to prayers with mil, and she likes their heads to be covered. I have learned to go along with it.
My husband is secular, and at home we are not religious. I actually like them going to mosque as it strengthens their relationship with mil, sharpens their Arabic, gives them another community, and teaches them some decent values.
Then when they come home I pick apart things they've been taught as doctrine, and we all argue discuss.
I don't know why I'm posting about our family situation, except that having contact with Islam as a non-muslim has been rewarding and enriching, as well as frustrating.
Good luck with her trip, I'm sure they won't eat her 