A Qatari women and girls must respect the tradition of her country her from my point of view and that is why she wear Abaya according to my opinion.
Some men whether they are Qatari or no may look and think bad thing of a woman what ever she is wearing.
The purpose of the dress in Islam is to cover and hid the sexual part of men or women.
Some people got affected and think badly when they see things infront of them.