Mobile Sim -  you gotta go to a QTel Shop and have a copy of your passport ready. QTel Shop is in City Center, Hyatt Plaza, Lulu (?). Also see http://www.qtel.com.qa/IndexPage.do;jsessionid=ac10968830d58975a8e7fc2b4771978fada85a1e9600.e34RbNiMc38RaO0PchuSa38Tb310n6jAmljGr5XDqQLvpAe

Laptop - Virgin Mega Store in Villaggio or Carrefour in Villaggio or City Center (Guess Carrefour is cheaper).