"It is merely copying Mummy and getting them used to idea of hejab for when they are older and they can choose to wear it or not"
Sorry love, but I fear you are being woefully naive. This IS done by uneducated and fervent muslims, thinking they are doing the right thing. I'm not saying these people are extremist, but they are nonetheless fundamentalists. The fear of evil westernisation
drives these people to be more and more dedicated.
It ISN'T right to decide to cover a 7yo girl, anymore than it's right to tell a woman she must wear the niqab. It HAS to be her choice , every single time, and at 7yo, I would doubt it IS her informed decision.
It IS conditioning.
As adults we can lead by example, the DD need not cover at all until she personally chooses to wear it... OR NOT....
But that never happens really, not in islamic countries anyway. It is expected of her, and she IS effectively brainwashed into wearing it. If nothing else, more often or not the Father or Brother tells her she is covering whether she wants to or not.