With other airlines, to order to claim for another person you usually have to submit a copy of their ID and a signed letter stating that you have their authority to claim on their behalf and receive the compensation on their behalf. Without this assertion Qatar could pony up the compensation to you and then the other passenger then puts their own claim in sometime later and there's a mess to sort out.

Although you might think it's better to do a joint claim, in reality it's probably easier to do two separate claims with the compensation being sent to each passenger separately.