Honestly? I wouldn't take my kids, I'm not a muslim and whilst I'm all for letting them be what they want to be when they are older, they can bloomin well do it when they are older.
I also wouldn't take my kid to a church for lessons even if they asked, or to a synagogue even if they asked, religion is something they can learn about when they are older, for now I'll stick to talking to them about things, letting them learn the same as other kids in school and taking them to the natural history museum.
It's you choice of course, but I must admit I can't quite wrap my head around why you would even be considering it.
Well I'm no expert in psychology, but I reckon if I keep refusing her pleas she will only romantacise and become more keen on going to the mosque.
This way, I hope she will see it is really quite boring. (I hated it when my dad took us to an Egyptian Sunday School for a while - it didn't last long lol)
The thing is this did not come out of the blue, she has been pestering me for ages about the "Islamic" side of things. Her mum is very religious and always goes on about it when they are with her. My daughter herself constantly tells people she is "Muslim" (or Arabic - same thing to her lol). She knows I don't believe and am not a Muslim now. Maybe its her way of challenging me - or perhaps keeping in touch with her mum who is not around (most of the time)
I think if I deny her the chance to explore her own identity a bit - I will only store up trouble for later. At least this way I am there to explain things from my point of view and guide her.