According to the CITES website (www.cites.org), the enforcement authorities for Qatar are contactable via the following:

Ministry of Environment
PO Box 7634
Doha

Telephone +974 420 7177
Fax +974 420 7839
Email [email protected] or [email protected]

As Chelsea said, you can report what you see to the authorities and they will confiscate them.

Hopefully one day there will be no more cases of animals at the souq or in the atrocious conditions that they are kept in at the various pet shops. If we all make enough noise and voice your opinions to shop owners and staff, potential buyers (see Chelsea's post above) and the authorities, this one day will be very soon.