There is no Dress code in Qatar.

There is Dress code in Saudi Arabia i.e women have to wear abhaya (a black cloth with or without design) on top of what they wear. I don't know abt head cover in Saudi but have seen ppl wearing just abhaya and not covering head. Whether ur local or non local or whether u r a muslim or non- muslim, u have to follow the dress code.

U dont have to be scared of Qatar or Saudi Arabia , its a normal country like any other country or even better in terms of social security.