most shops in the malls would be open from 10am till around 1pm.
then in the evening, after Iftar (around 8pm).
Some stay open even until midnight.

However, supermarkets, like Carrefour, are open longer.
It is not posted on the web site yet what are the working hours during Ramadan, but here is a link to the web site with info, u can give them a call for details:
http://www.carrefourqatar.com/Site/carrefourqatar/English/aboutus-main.asp