Wrong. The aurah of men and women is described in ahadith of Prophet Muhammad(SAW). Also, the word khimar used in Quran means head scarf.
Covering head is also prescribed in other Abrahamic religions so there's no doubt in that.....but if woman fears harrassment and abuse in a Western culture then she can take off head scarf.
It says khimar should be used to cover breast part because tradion was to cover that part with ornaments which otherwise used to be bare, but there is no mention of burqua as people know as of today..